% Mizar ND problem: t7_jordan2c,jordan2c,116,33 fof(dh_c1_5__jordan2c,definition, ( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( k2_relat_1(B) = k2_tarski(c1_5__jordan2c,A) & k3_finseq_1(B) = 2 & ~ ( k1_funct_1(B,1) = c1_5__jordan2c & k1_funct_1(B,2) = A ) & ~ ( k1_funct_1(B,1) = A & k1_funct_1(B,2) = c1_5__jordan2c ) ) ) => ! [C,D,E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ~ ( k2_relat_1(E) = k2_tarski(C,D) & k3_finseq_1(E) = 2 & ~ ( k1_funct_1(E,1) = C & k1_funct_1(E,2) = D ) & ~ ( k1_funct_1(E,1) = D & k1_funct_1(E,2) = C ) ) ) ), introduced(definition,[new_symbol(c1_5__jordan2c),file(jordan2c,c1_5__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,c1_5__jordan2c)]). fof(dh_c2_5__jordan2c,definition, ( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ~ ( k2_relat_1(A) = k2_tarski(c1_5__jordan2c,c2_5__jordan2c) & k3_finseq_1(A) = 2 & ~ ( k1_funct_1(A,1) = c1_5__jordan2c & k1_funct_1(A,2) = c2_5__jordan2c ) & ~ ( k1_funct_1(A,1) = c2_5__jordan2c & k1_funct_1(A,2) = c1_5__jordan2c ) ) ) => ! [B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( k2_relat_1(C) = k2_tarski(c1_5__jordan2c,B) & k3_finseq_1(C) = 2 & ~ ( k1_funct_1(C,1) = c1_5__jordan2c & k1_funct_1(C,2) = B ) & ~ ( k1_funct_1(C,1) = B & k1_funct_1(C,2) = c1_5__jordan2c ) ) ) ), introduced(definition,[new_symbol(c2_5__jordan2c),file(jordan2c,c2_5__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,c2_5__jordan2c)]). fof(dh_c3_5__jordan2c,definition, ( ( ( v1_relat_1(c3_5__jordan2c) & v1_funct_1(c3_5__jordan2c) & v1_finseq_1(c3_5__jordan2c) ) => ~ ( k2_relat_1(c3_5__jordan2c) = k2_tarski(c1_5__jordan2c,c2_5__jordan2c) & k3_finseq_1(c3_5__jordan2c) = 2 & ~ ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ) & ~ ( k1_funct_1(c3_5__jordan2c,1) = c2_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c1_5__jordan2c ) ) ) => ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ~ ( k2_relat_1(A) = k2_tarski(c1_5__jordan2c,c2_5__jordan2c) & k3_finseq_1(A) = 2 & ~ ( k1_funct_1(A,1) = c1_5__jordan2c & k1_funct_1(A,2) = c2_5__jordan2c ) & ~ ( k1_funct_1(A,1) = c2_5__jordan2c & k1_funct_1(A,2) = c1_5__jordan2c ) ) ) ), introduced(definition,[new_symbol(c3_5__jordan2c),file(jordan2c,c3_5__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,c3_5__jordan2c)]). fof(e1_5__jordan2c,assumption, ( k2_relat_1(c3_5__jordan2c) = k2_tarski(c1_5__jordan2c,c2_5__jordan2c) & k3_finseq_1(c3_5__jordan2c) = 2 ), introduced(assumption,[file(jordan2c,e1_5__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,e1_5__jordan2c)]). fof(cc4_xreal_0,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) ) ) ), file(xreal_0,cc4_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc4_xreal_0)]). fof(cc5_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & v3_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) ) ), file(xreal_0,cc5_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc5_xreal_0)]). fof(cc8_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) => ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(xreal_0,cc8_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc8_xreal_0)]). fof(rc2_xreal_0,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc2_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc2_xreal_0)]). fof(rc3_xreal_0,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & v3_xreal_0(A) ) ), file(xreal_0,rc3_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc3_xreal_0)]). fof(rc4_xreal_0,theorem,( ? [A] : ( v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ), file(xreal_0,rc4_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc4_xreal_0)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(cc1_arytm_3,theorem,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) ) ) ) ), file(arytm_3,cc1_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]). fof(cc1_xreal_0,theorem,( ! [A] : ( v4_ordinal2(A) => v1_xreal_0(A) ) ), file(xreal_0,cc1_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc1_xreal_0)]). fof(cc2_arytm_3,theorem,( ! [A] : ( ( v1_xboole_0(A) & v3_ordinal1(A) ) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc2_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]). fof(cc2_xreal_0,theorem,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) ), file(xreal_0,cc2_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc2_xreal_0)]). fof(cc3_xreal_0,theorem,( ! [A] : ( ( v1_xreal_0(A) & v2_xreal_0(A) ) => ( ~ v1_xboole_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc3_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc3_xreal_0)]). fof(cc6_xreal_0,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v3_xreal_0(A) ) ) ), file(xreal_0,cc6_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc6_xreal_0)]). fof(cc7_xreal_0,theorem,( ! [A] : ( ( v1_xboole_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & ~ v2_xreal_0(A) & ~ v3_xreal_0(A) ) ) ), file(xreal_0,cc7_xreal_0), [interesting(0.9),axiom,file(xreal_0,cc7_xreal_0)]). fof(fc12_membered,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) ), file(membered,fc12_membered), [interesting(0.9),axiom,file(membered,fc12_membered)]). fof(fc13_membered,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) ) ) ), file(membered,fc13_membered), [interesting(0.9),axiom,file(membered,fc13_membered)]). fof(fc14_membered,theorem,( ! [A,B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) ) ) ), file(membered,fc14_membered), [interesting(0.9),axiom,file(membered,fc14_membered)]). fof(fc15_membered,theorem,( ! [A,B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) ) ) ), file(membered,fc15_membered), [interesting(0.9),axiom,file(membered,fc15_membered)]). fof(fc16_membered,theorem,( ! [A,B] : ( ( v4_ordinal2(A) & v4_ordinal2(B) ) => ( v1_membered(k2_tarski(A,B)) & v2_membered(k2_tarski(A,B)) & v3_membered(k2_tarski(A,B)) & v4_membered(k2_tarski(A,B)) & v5_membered(k2_tarski(A,B)) ) ) ), file(membered,fc16_membered), [interesting(0.9),axiom,file(membered,fc16_membered)]). fof(rc1_arytm_3,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ), file(arytm_3,rc1_arytm_3), [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]). fof(rc1_xreal_0,theorem,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ), file(xreal_0,rc1_xreal_0), [interesting(0.9),axiom,file(xreal_0,rc1_xreal_0)]). fof(rc2_finset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & v4_ordinal2(B) & v1_finset_1(B) ) ), file(finset_1,rc2_finset_1), [interesting(0.9),axiom,file(finset_1,rc2_finset_1)]). fof(rc4_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc4_funct_1), [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]). fof(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). fof(dt_k1_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). fof(cc10_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) ), file(membered,cc10_membered), [interesting(0.9),axiom,file(membered,cc10_membered)]). fof(cc11_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) ) ) ) ), file(membered,cc11_membered), [interesting(0.9),axiom,file(membered,cc11_membered)]). fof(cc12_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_rat_1(B) ) ) ) ), file(membered,cc12_membered), [interesting(0.9),axiom,file(membered,cc12_membered)]). fof(cc13_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc13_membered), [interesting(0.9),axiom,file(membered,cc13_membered)]). fof(cc14_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_xcmplx_0(B) & v4_ordinal2(B) & v1_xreal_0(B) & v1_int_1(B) & v1_rat_1(B) ) ) ) ), file(membered,cc14_membered), [interesting(0.9),axiom,file(membered,cc14_membered)]). fof(cc16_membered,theorem,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) ), file(membered,cc16_membered), [interesting(0.9),axiom,file(membered,cc16_membered)]). fof(cc17_membered,theorem,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) ) ) ) ), file(membered,cc17_membered), [interesting(0.9),axiom,file(membered,cc17_membered)]). fof(cc18_membered,theorem,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) ) ) ) ), file(membered,cc18_membered), [interesting(0.9),axiom,file(membered,cc18_membered)]). fof(cc19_membered,theorem,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) ) ) ) ), file(membered,cc19_membered), [interesting(0.9),axiom,file(membered,cc19_membered)]). fof(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). fof(cc20_membered,theorem,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_membered(B) & v2_membered(B) & v3_membered(B) & v4_membered(B) & v5_membered(B) ) ) ) ), file(membered,cc20_membered), [interesting(0.9),axiom,file(membered,cc20_membered)]). fof(cc2_finset_1,theorem,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) ), file(finset_1,cc2_finset_1), [interesting(0.9),axiom,file(finset_1,cc2_finset_1)]). fof(cc2_membered,theorem,( ! [A] : ( v4_membered(A) => v3_membered(A) ) ), file(membered,cc2_membered), [interesting(0.9),axiom,file(membered,cc2_membered)]). fof(cc3_arytm_3,theorem,( ! [A] : ( m1_subset_1(A,k5_ordinal2) => ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal2(A) ) ) ), file(arytm_3,cc3_arytm_3), [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]). fof(cc3_membered,theorem,( ! [A] : ( v3_membered(A) => v2_membered(A) ) ), file(membered,cc3_membered), [interesting(0.9),axiom,file(membered,cc3_membered)]). fof(cc4_membered,theorem,( ! [A] : ( v2_membered(A) => v1_membered(A) ) ), file(membered,cc4_membered), [interesting(0.9),axiom,file(membered,cc4_membered)]). fof(cc6_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_membered(A) & v2_membered(A) ) ) ), file(membered,cc6_membered), [interesting(0.9),axiom,file(membered,cc6_membered)]). fof(cc9_membered,theorem,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_numbers)) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc9_membered), [interesting(0.9),axiom,file(membered,cc9_membered)]). fof(fc1_subset_1,theorem,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ), file(subset_1,fc1_subset_1), [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]). fof(fc2_finseq_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) & v1_funct_1(k1_xboole_0) & v2_funct_1(k1_xboole_0) & v1_finset_1(k1_xboole_0) & v1_finseq_1(k1_xboole_0) ), file(finseq_1,fc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]). fof(fc5_membered,theorem, ( v1_membered(k5_ordinal2) & v2_membered(k5_ordinal2) & v3_membered(k5_ordinal2) & v4_membered(k5_ordinal2) & v5_membered(k5_ordinal2) ), file(membered,fc5_membered), [interesting(0.9),axiom,file(membered,fc5_membered)]). fof(fc6_membered,theorem, ( v1_xboole_0(k1_xboole_0) & v1_membered(k1_xboole_0) & v2_membered(k1_xboole_0) & v3_membered(k1_xboole_0) & v4_membered(k1_xboole_0) & v5_membered(k1_xboole_0) ), file(membered,fc6_membered), [interesting(0.9),axiom,file(membered,fc6_membered)]). fof(rc1_membered,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ), file(membered,rc1_membered), [interesting(0.9),axiom,file(membered,rc1_membered)]). fof(rc1_subset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) ), file(subset_1,rc1_subset_1), [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]). fof(rc2_subset_1,theorem,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) ), file(subset_1,rc2_subset_1), [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]). fof(rc3_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc3_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]). fof(rc3_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc3_finset_1), [interesting(0.9),axiom,file(finset_1,rc3_finset_1)]). fof(rc3_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(funct_1,rc3_funct_1), [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]). fof(rc4_finset_1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ), file(finset_1,rc4_finset_1), [interesting(0.9),axiom,file(finset_1,rc4_finset_1)]). fof(rc6_finseq_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc6_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]). fof(t3_subset,theorem,( ! [A,B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) ), file(subset,t3_subset), [interesting(0.9),axiom,file(subset,t3_subset)]). fof(t4_subset,theorem,( ! [A,B,C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) ), file(subset,t4_subset), [interesting(0.9),axiom,file(subset,t4_subset)]). fof(t5_subset,theorem,( ! [A,B,C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) ), file(subset,t5_subset), [interesting(0.9),axiom,file(subset,t5_subset)]). fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(existence_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(redefinition_m2_subset_1,definition,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) ), file(card_1,k1_card_1), [interesting(0.9),axiom,file(card_1,k1_card_1)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_subset_1)]). fof(dt_m2_subset_1,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) ), file(subset_1,m2_subset_1), [interesting(0.9),axiom,file(subset_1,m2_subset_1)]). fof(cc15_membered,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) ) ) ), file(membered,cc15_membered), [interesting(0.9),axiom,file(membered,cc15_membered)]). fof(cc1_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) ), file(finseq_1,cc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]). fof(cc1_finset_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) ), file(finset_1,cc1_finset_1), [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]). fof(cc1_funct_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) ), file(funct_1,cc1_funct_1), [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]). fof(cc2_funct_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) ), file(funct_1,cc2_funct_1), [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]). fof(fc11_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k2_relat_1(A)) ) ), file(finseq_1,fc11_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]). fof(fc2_membered,theorem, ( ~ v1_xboole_0(k1_numbers) & v1_membered(k1_numbers) & v2_membered(k1_numbers) ), file(membered,fc2_membered), [interesting(0.9),axiom,file(membered,fc2_membered)]). fof(rc1_finseq_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]). fof(rc1_finset_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) ), file(finset_1,rc1_finset_1), [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]). fof(rc1_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) ), file(funct_1,rc1_funct_1), [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]). fof(rc2_funct_1,theorem,( ? [A] : ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) ), file(funct_1,rc2_funct_1), [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]). fof(rc7_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ), file(finseq_1,rc7_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]). fof(rc8_finseq_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) ) ), file(finseq_1,rc8_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]). fof(t2_subset,theorem,( ! [A,B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) ), file(subset,t2_subset), [interesting(0.9),axiom,file(subset,t2_subset)]). fof(t6_boole,theorem,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) ), file(boole,t6_boole), [interesting(0.9),axiom,file(boole,t6_boole)]). fof(t8_boole,theorem,( ! [A,B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) ), file(boole,t8_boole), [interesting(0.9),axiom,file(boole,t8_boole)]). fof(commutativity_k2_tarski,theorem,( ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(antisymmetry_r2_hidden,theorem,( ! [A,B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) ), file(hidden,r2_hidden), [interesting(0.9),axiom,file(hidden,r2_hidden)]). fof(redefinition_k3_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) ), file(finseq_1,k3_finseq_1), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(dt_k1_funct_1,axiom,( $true ), file(funct_1,k1_funct_1), [interesting(0.9),axiom,file(funct_1,k1_funct_1)]). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), [interesting(0.9),axiom,file(relat_1,k2_relat_1)]). fof(dt_k2_tarski,axiom,( $true ), file(tarski,k2_tarski), [interesting(0.9),axiom,file(tarski,k2_tarski)]). fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ), file(finseq_1,k3_finseq_1), [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]). fof(dt_c1_5__jordan2c,assumption,( $true ), introduced(assumption,[file(jordan2c,c1_5__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,c1_5__jordan2c)]). fof(dt_c2_5__jordan2c,assumption,( $true ), introduced(assumption,[file(jordan2c,c2_5__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,c2_5__jordan2c)]). fof(dt_c3_5__jordan2c,assumption, ( v1_relat_1(c3_5__jordan2c) & v1_funct_1(c3_5__jordan2c) & v1_finseq_1(c3_5__jordan2c) ), introduced(assumption,[file(jordan2c,c3_5__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,c3_5__jordan2c)]). fof(fc2_finset_1,theorem,( ! [A,B] : ( ~ v1_xboole_0(k2_tarski(A,B)) & v1_finset_1(k2_tarski(A,B)) ) ), file(finset_1,fc2_finset_1), [interesting(0.9),axiom,file(finset_1,fc2_finset_1)]). fof(fc3_subset_1,theorem,( ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ), file(subset_1,fc3_subset_1), [interesting(0.9),axiom,file(subset_1,fc3_subset_1)]). fof(t1_subset,theorem,( ! [A,B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) ), file(subset,t1_subset), [interesting(0.9),axiom,file(subset,t1_subset)]). fof(t7_boole,theorem,( ! [A,B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) ), file(boole,t7_boole), [interesting(0.9),axiom,file(boole,t7_boole)]). fof(spc1_numerals,theorem, ( v2_xreal_0(1) & m2_subset_1(1,k1_numbers,k5_numbers) & m1_subset_1(1,k5_numbers) & m1_subset_1(1,k1_numbers) ), file(numerals,spc1_numerals), [interesting(0.9),axiom,file(numerals,spc1_numerals)]). fof(spc2_numerals,theorem, ( v2_xreal_0(2) & m2_subset_1(2,k1_numbers,k5_numbers) & m1_subset_1(2,k5_numbers) & m1_subset_1(2,k1_numbers) ), file(numerals,spc2_numerals), [interesting(0.9),axiom,file(numerals,spc2_numerals)]). fof(spc1_boole,theorem,( ~ v1_xboole_0(1) ), file(boole,spc1_boole), [interesting(0.9),axiom,file(boole,spc1_boole)]). fof(spc2_boole,theorem,( ~ v1_xboole_0(2) ), file(boole,spc2_boole), [interesting(0.9),axiom,file(boole,spc2_boole)]). fof(e1_5_2__jordan2c,assumption, ( k1_funct_1(c3_5__jordan2c,1) = c2_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ), introduced(assumption,[file(jordan2c,e1_5_2__jordan2c)]), [interesting(0.65),axiom,file(jordan2c,e1_5_2__jordan2c)]). fof(e1_5_2_1_1__jordan2c,assumption,( c2_5_2__jordan2c = 1 ), introduced(assumption,[file(jordan2c,e1_5_2_1_1__jordan2c)]), [interesting(0.35),axiom,file(jordan2c,e1_5_2_1_1__jordan2c)]). fof(fc17_finseq_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) ), file(finseq_1,fc17_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(redefinition_k4_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k1_relat_1(A) ) ), file(finseq_1,k4_finseq_1), [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]). fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k4_finseq_1), [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]). fof(dh_c1_5_2__jordan2c,definition, ( ? [A] : ( r2_hidden(A,k4_finseq_1(c3_5__jordan2c)) & c1_5__jordan2c = k1_funct_1(c3_5__jordan2c,A) ) => ( r2_hidden(c1_5_2__jordan2c,k4_finseq_1(c3_5__jordan2c)) & c1_5__jordan2c = k1_funct_1(c3_5__jordan2c,c1_5_2__jordan2c) ) ), introduced(definition,[new_symbol(c1_5_2__jordan2c),file(jordan2c,c1_5_2__jordan2c)]), [interesting(0.65),axiom,file(jordan2c,c1_5_2__jordan2c)]). fof(d2_tarski,definition,( ! [A,B,C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) ), file(tarski,d2_tarski), [interesting(0.9),axiom,file(tarski,d2_tarski)]). fof(e2_5_2__jordan2c,plain,( r2_hidden(c1_5__jordan2c,k2_relat_1(c3_5__jordan2c)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_arytm_3,rc1_xreal_0,rc2_finset_1,rc4_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc11_finseq_1,fc2_membered,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k3_finseq_1,dt_k2_relat_1,dt_k2_tarski,dt_k3_finseq_1,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,fc2_finset_1,fc3_subset_1,t1_subset,t7_boole,spc2_numerals,spc2_boole,e1_5__jordan2c,d2_tarski]), [interesting(0.65),file(jordan2c,e2_5_2__jordan2c),[file(jordan2c,e2_5_2__jordan2c)]]). fof(d5_funct_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k2_relat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k1_relat_1(A)) & C = k1_funct_1(A,D) ) ) ) ) ), file(funct_1,d5_funct_1), [interesting(0.9),axiom,file(funct_1,d5_funct_1)]). fof(e3_5_2__jordan2c,plain,( ? [A] : ( r2_hidden(A,k4_finseq_1(c3_5__jordan2c)) & c1_5__jordan2c = k1_funct_1(c3_5__jordan2c,A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xreal_0,cc7_xreal_0,rc1_arytm_3,rc1_xreal_0,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_numbers,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,redefinition_k5_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc9_membered,fc1_subset_1,rc1_finseq_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_finseq_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k4_finseq_1,dt_c1_5__jordan2c,dt_c3_5__jordan2c,rc1_funct_1,t1_subset,t7_boole,e2_5_2__jordan2c,d5_funct_1]), [interesting(0.65),file(jordan2c,e3_5_2__jordan2c),[file(jordan2c,e3_5_2__jordan2c)]]). fof(dt_c1_5_2__jordan2c,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[dh_c1_5_2__jordan2c,e3_5_2__jordan2c]), [interesting(0.65),file(jordan2c,c1_5_2__jordan2c),[file(jordan2c,c1_5_2__jordan2c)]]). fof(de_c2_5_2__jordan2c,definition,( c2_5_2__jordan2c = c1_5_2__jordan2c ), introduced(definition,[new_symbol(c2_5_2__jordan2c),file(jordan2c,c2_5_2__jordan2c)]), [interesting(0.65),axiom,file(jordan2c,c2_5_2__jordan2c)]). fof(e4_5_2__jordan2c,plain, ( r2_hidden(c1_5_2__jordan2c,k4_finseq_1(c3_5__jordan2c)) & c1_5__jordan2c = k1_funct_1(c3_5__jordan2c,c1_5_2__jordan2c) ), inference(consider,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[dh_c1_5_2__jordan2c,e3_5_2__jordan2c]), [interesting(0.65),file(jordan2c,e4_5_2__jordan2c),[file(jordan2c,e4_5_2__jordan2c)]]). fof(e6_5_2__jordan2c,plain,( m2_subset_1(c1_5_2__jordan2c,k1_numbers,k5_numbers) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc17_finseq_1,fc2_finseq_1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc1_xreal_0,rc2_finset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,rc1_finseq_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_5__jordan2c,dt_c1_5_2__jordan2c,dt_c3_5__jordan2c,fc2_membered,t1_subset,t7_boole,e4_5_2__jordan2c]), [interesting(0.65),file(jordan2c,e6_5_2__jordan2c),[file(jordan2c,e6_5_2__jordan2c)]]). fof(dt_c2_5_2__jordan2c,plain,( m2_subset_1(c2_5_2__jordan2c,k1_numbers,k5_numbers) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc1_finseq_1,cc2_funct_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc2_finseq_1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc1_xreal_0,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_subset_1,dt_c1_5_2__jordan2c,fc2_membered,de_c2_5_2__jordan2c,e6_5_2__jordan2c]), [interesting(0.65),file(jordan2c,c2_5_2__jordan2c),[file(jordan2c,c2_5_2__jordan2c)]]). fof(e2_5_2_1_1__jordan2c,plain, ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ), inference(mizar_by,[status(thm),assumptions([e1_5_2_1_1__jordan2c,e1_5_2__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_arytm_3,rc1_xreal_0,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,fc17_finseq_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,rc1_finseq_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_finseq_1,dt_k1_funct_1,dt_k4_finseq_1,dt_c1_5__jordan2c,dt_c1_5_2__jordan2c,dt_c2_5__jordan2c,dt_c2_5_2__jordan2c,dt_c3_5__jordan2c,de_c2_5_2__jordan2c,t1_subset,t7_boole,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e1_5_2_1_1__jordan2c,e1_5_2__jordan2c,e4_5_2__jordan2c]), [interesting(0.35),file(jordan2c,e2_5_2_1_1__jordan2c),[file(jordan2c,e2_5_2_1_1__jordan2c)]]). fof(i2_5_2_1_1__jordan2c,theorem,( $true ), introduced(tautology,[file(jordan2c,i2_5_2_1_1__jordan2c)]), [interesting(0.35),trivial,file(jordan2c,i2_5_2_1_1__jordan2c)]). fof(i1_5_2_1_1__jordan2c,plain, ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ), inference(conclusion,[status(thm),assumptions([e1_5_2_1_1__jordan2c,e1_5_2__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[e2_5_2_1_1__jordan2c,i2_5_2_1_1__jordan2c]), [interesting(0.35),file(jordan2c,i1_5_2_1_1__jordan2c),[file(jordan2c,i1_5_2_1_1__jordan2c)]]). fof(i1_5_2_1__jordan2c,plain, ( c2_5_2__jordan2c = 1 => ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ) ), inference(discharge_asm,[status(thm),assumptions([e1_5_2__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c]),discharge_asm(discharge,[e1_5_2_1_1__jordan2c])],[e1_5_2_1_1__jordan2c,i1_5_2_1_1__jordan2c]), [interesting(0.5),file(jordan2c,i1_5_2_1__jordan2c),[file(jordan2c,i1_5_2_1__jordan2c)]]). fof(e1_5_2_1_2__jordan2c,assumption,( c2_5_2__jordan2c = k23_binop_2(1,1) ), introduced(assumption,[file(jordan2c,e1_5_2_1_2__jordan2c)]), [interesting(0.35),axiom,file(jordan2c,e1_5_2_1_2__jordan2c)]). fof(fc10_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & v2_xreal_0(k2_xcmplx_0(B,A)) & ~ v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc10_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc10_xreal_0)]). fof(fc11_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) & v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc11_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc11_xreal_0)]). fof(fc12_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v3_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(B,A)) & v1_xcmplx_0(k2_xcmplx_0(B,A)) & v1_xreal_0(k2_xcmplx_0(B,A)) & ~ v2_xreal_0(k2_xcmplx_0(B,A)) & v3_xreal_0(k2_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc12_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc12_xreal_0)]). fof(fc21_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v2_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc21_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc21_xreal_0)]). fof(fc22_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(B,A)) & v1_xreal_0(k3_xcmplx_0(B,A)) & ~ v2_xreal_0(k3_xcmplx_0(B,A)) ) ) ), file(xreal_0,fc22_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc22_xreal_0)]). fof(fc24_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc24_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc24_xreal_0)]). fof(fc7_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v3_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc7_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc7_xreal_0)]). fof(fc9_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v2_xreal_0(A) & v1_xreal_0(B) & ~ v3_xreal_0(B) ) => ( ~ v1_xboole_0(k2_xcmplx_0(A,B)) & v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & v2_xreal_0(k2_xcmplx_0(A,B)) & ~ v3_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc9_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc9_xreal_0)]). fof(fc23_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) & ~ v3_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc23_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc23_xreal_0)]). fof(fc3_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc3_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc3_xreal_0)]). fof(fc4_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xcmplx_0(k3_xcmplx_0(A,B)) & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc4_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc4_xreal_0)]). fof(fc8_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & ~ v2_xreal_0(A) & v1_xreal_0(B) & ~ v2_xreal_0(B) ) => ( v1_xcmplx_0(k2_xcmplx_0(A,B)) & v1_xreal_0(k2_xcmplx_0(A,B)) & ~ v2_xreal_0(k2_xcmplx_0(A,B)) ) ) ), file(xreal_0,fc8_xreal_0), [interesting(0.9),axiom,file(xreal_0,fc8_xreal_0)]). fof(spc5_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ), file(arithm,spc5_arithm), [interesting(0.9),axiom,file(arithm,spc5_arithm)]). fof(spc6_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(spc7_arithm,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k3_xcmplx_0(B,C)) ) ), file(arithm,spc6_arithm), [interesting(0.9),axiom,file(arithm,spc6_arithm)]). fof(t3_arithm,theorem,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) ), file(arithm,t3_arithm), [interesting(0.9),axiom,file(arithm,t3_arithm)]). fof(commutativity_k23_binop_2,theorem,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k23_binop_2(A,B) = k23_binop_2(B,A) ) ), file(binop_2,k23_binop_2), [interesting(0.9),axiom,file(binop_2,k23_binop_2)]). fof(commutativity_k2_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(commutativity_k3_xcmplx_0,theorem,( ! [A,B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]). fof(redefinition_k23_binop_2,definition,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => k23_binop_2(A,B) = k2_xcmplx_0(A,B) ) ), file(binop_2,k23_binop_2), [interesting(0.9),axiom,file(binop_2,k23_binop_2)]). fof(dt_k23_binop_2,axiom,( ! [A,B] : ( ( m1_subset_1(A,k5_numbers) & m1_subset_1(B,k5_numbers) ) => m2_subset_1(k23_binop_2(A,B),k1_numbers,k5_numbers) ) ), file(binop_2,k23_binop_2), [interesting(0.9),axiom,file(binop_2,k23_binop_2)]). fof(dt_k2_xcmplx_0,axiom,( $true ), file(xcmplx_0,k2_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k2_xcmplx_0)]). fof(dt_k3_xcmplx_0,axiom,( $true ), file(xcmplx_0,k3_xcmplx_0), [interesting(0.9),axiom,file(xcmplx_0,k3_xcmplx_0)]). fof(rqRealMult__k3_xcmplx_0__r1_r1_r1,theorem,( k3_xcmplx_0(1,1) = 1 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r1_r1)]). fof(rqRealMult__k3_xcmplx_0__r1_r2_r2,theorem,( k3_xcmplx_0(1,2) = 2 ), file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r1_r2_r2)]). fof(rqRealAdd__k2_xcmplx_0__r1_r1_r2,theorem,( k2_xcmplx_0(1,1) = 2 ), file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealAdd__k2_xcmplx_0__r1_r1_r2)]). fof(rqRealMult__k3_xcmplx_0__r2_r1_r2,theorem,( k3_xcmplx_0(2,1) = 2 ), file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2), [interesting(0.9),axiom,file(arithm,rqRealMult__k3_xcmplx_0__r2_r1_r2)]). fof(e2_5_2_1_2__jordan2c,plain, ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ), inference(mizar_by,[status(thm),assumptions([e1_5_2_1_2__jordan2c,e1_5_2__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc7_xreal_0,fc9_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc3_xreal_0,fc4_xreal_0,fc8_xreal_0,rc1_arytm_3,rc1_xreal_0,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,fc17_finseq_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,rc1_finseq_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,spc5_arithm,spc6_arithm,spc7_arithm,t2_subset,t3_arithm,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k23_binop_2,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,antisymmetry_r2_hidden,redefinition_k23_binop_2,redefinition_k4_finseq_1,dt_k1_funct_1,dt_k23_binop_2,dt_k2_xcmplx_0,dt_k3_xcmplx_0,dt_k4_finseq_1,dt_c1_5__jordan2c,dt_c1_5_2__jordan2c,dt_c2_5__jordan2c,dt_c2_5_2__jordan2c,dt_c3_5__jordan2c,de_c2_5_2__jordan2c,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,t1_subset,t7_boole,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e1_5_2_1_2__jordan2c,e1_5_2__jordan2c,e4_5_2__jordan2c,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2]), [interesting(0.35),file(jordan2c,e2_5_2_1_2__jordan2c),[file(jordan2c,e2_5_2_1_2__jordan2c)]]). fof(i2_5_2_1_2__jordan2c,theorem,( $true ), introduced(tautology,[file(jordan2c,i2_5_2_1_2__jordan2c)]), [interesting(0.35),trivial,file(jordan2c,i2_5_2_1_2__jordan2c)]). fof(i1_5_2_1_2__jordan2c,plain, ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ), inference(conclusion,[status(thm),assumptions([e1_5_2_1_2__jordan2c,e1_5_2__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[e2_5_2_1_2__jordan2c,i2_5_2_1_2__jordan2c]), [interesting(0.35),file(jordan2c,i1_5_2_1_2__jordan2c),[file(jordan2c,i1_5_2_1_2__jordan2c)]]). fof(i2_5_2_1__jordan2c,plain, ( c2_5_2__jordan2c = k23_binop_2(1,1) => ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ) ), inference(discharge_asm,[status(thm),assumptions([e1_5_2__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c]),discharge_asm(discharge,[e1_5_2_1_2__jordan2c])],[e1_5_2_1_2__jordan2c,i1_5_2_1_2__jordan2c]), [interesting(0.5),file(jordan2c,i2_5_2_1__jordan2c),[file(jordan2c,i2_5_2_1__jordan2c)]]). fof(t2_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v3_xreal_0(B) ) => v3_xreal_0(A) ) ) ) ), file(real,t2_real), [interesting(0.9),axiom,file(real,t2_real)]). fof(t3_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v3_xreal_0(A) & v3_xreal_0(B) ) ) ) ), file(real,t3_real), [interesting(0.9),axiom,file(real,t3_real)]). fof(t5_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(B) | v3_xreal_0(A) | v2_xreal_0(B) ) ) ) ) ), file(real,t5_real), [interesting(0.9),axiom,file(real,t5_real)]). fof(t6_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xreal_0(A,B) => ( v1_xboole_0(A) | v2_xreal_0(B) | v3_xreal_0(A) ) ) ) ) ), file(real,t6_real), [interesting(0.9),axiom,file(real,t6_real)]). fof(t7_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v2_xreal_0(A) & ~ v3_xreal_0(B) ) ) ) ), file(real,t7_real), [interesting(0.9),axiom,file(real,t7_real)]). fof(t8_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xreal_0(A,B) & ~ v3_xreal_0(B) & ~ v2_xreal_0(A) ) ) ) ), file(real,t8_real), [interesting(0.9),axiom,file(real,t8_real)]). fof(t1_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xreal_0(A,B) & v2_xreal_0(A) ) => v2_xreal_0(B) ) ) ) ), file(real,t1_real), [interesting(0.9),axiom,file(real,t1_real)]). fof(t4_real,theorem,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xreal_0(A,B) & ~ v2_xreal_0(B) & v2_xreal_0(A) ) ) ) ), file(real,t4_real), [interesting(0.9),axiom,file(real,t4_real)]). fof(reflexivity_r1_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => r1_xreal_0(A,A) ) ), file(xreal_0,r1_xreal_0), [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]). fof(connectedness_r1_xreal_0,theorem,( ! [A,B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( r1_xreal_0(A,B) | r1_xreal_0(B,A) ) ) ), file(xreal_0,r1_xreal_0), [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]). fof(rqLessOrEqual__r1_xreal_0__r2_r1,theorem,( ~ r1_xreal_0(2,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r1)]). fof(dt_k1_finseq_1,axiom,( $true ), file(finseq_1,k1_finseq_1), [interesting(0.9),axiom,file(finseq_1,k1_finseq_1)]). fof(fc1_finseq_1,theorem,( ! [A] : ( v4_ordinal2(A) => v1_finset_1(k1_finseq_1(A)) ) ), file(finseq_1,fc1_finseq_1), [interesting(0.9),axiom,file(finseq_1,fc1_finseq_1)]). fof(redefinition_k2_finseq_1,definition,( ! [A] : ( v4_ordinal2(A) => k2_finseq_1(A) = k1_finseq_1(A) ) ), file(finseq_1,k2_finseq_1), [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]). fof(dt_k2_finseq_1,axiom,( ! [A] : ( v4_ordinal2(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ), file(finseq_1,k2_finseq_1), [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]). fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,( r1_xreal_0(1,1) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]). fof(d3_finseq_1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ), file(finseq_1,d3_finseq_1), [interesting(0.9),axiom,file(finseq_1,d3_finseq_1)]). fof(e5_5_2__jordan2c,plain,( r2_hidden(c1_5_2__jordan2c,k2_finseq_1(k3_finseq_1(c3_5__jordan2c))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc20_membered,cc2_arytm_3,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc2_finseq_1,fc6_membered,rc1_arytm_3,rc1_membered,rc1_xreal_0,rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_finseq_1,fc1_subset_1,fc5_membered,rc1_finset_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_5__jordan2c,dt_c1_5_2__jordan2c,dt_c3_5__jordan2c,cc1_finseq_1,fc2_membered,rc1_finseq_1,rc1_funct_1,t1_subset,t7_boole,e4_5_2__jordan2c,d3_finseq_1]), [interesting(0.65),file(jordan2c,e5_5_2__jordan2c),[file(jordan2c,e5_5_2__jordan2c)]]). fof(t3_finseq_1,theorem,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ( r2_hidden(A,k2_finseq_1(B)) <=> ( r1_xreal_0(1,A) & r1_xreal_0(A,B) ) ) ) ) ), file(finseq_1,t3_finseq_1), [interesting(0.9),axiom,file(finseq_1,t3_finseq_1)]). fof(e7_5_2__jordan2c,plain, ( r1_xreal_0(1,c2_5_2__jordan2c) & r1_xreal_0(c2_5_2__jordan2c,k3_finseq_1(c3_5__jordan2c)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc1_xreal_0,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc2_xreal_0,cc3_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_finseq_1,fc1_subset_1,fc2_membered,rc1_finseq_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k2_finseq_1,redefinition_k3_finseq_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_c1_5_2__jordan2c,dt_c2_5_2__jordan2c,dt_c3_5__jordan2c,de_c2_5_2__jordan2c,cc1_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e5_5_2__jordan2c,t3_finseq_1]), [interesting(0.65),file(jordan2c,e7_5_2__jordan2c),[file(jordan2c,e7_5_2__jordan2c)]]). fof(t27_nat_1,theorem,( ! [A] : ( v4_ordinal2(A) => ! [B] : ( v4_ordinal2(B) => ~ ( r1_xreal_0(A,B) & r1_xreal_0(B,k2_xcmplx_0(A,1)) & A != B & B != k2_xcmplx_0(A,1) ) ) ) ), file(nat_1,t27_nat_1), [interesting(0.9),axiom,file(nat_1,t27_nat_1)]). fof(rqLessOrEqual__r1_xreal_0__r2_r2,theorem,( r1_xreal_0(2,2) ), file(arithm,rqLessOrEqual__r1_xreal_0__r2_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r2_r2)]). fof(rqLessOrEqual__r1_xreal_0__r1_r2,theorem,( r1_xreal_0(1,2) ), file(arithm,rqLessOrEqual__r1_xreal_0__r1_r2), [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r2)]). fof(e1_5_2_1__jordan2c,plain, ( c2_5_2__jordan2c = 1 | c2_5_2__jordan2c = k23_binop_2(1,1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[reflexivity_r1_tarski,cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,rc2_finset_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc20_membered,cc2_finset_1,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_membered,fc15_membered,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_finseq_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc6_finseq_1,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c1_5_2__jordan2c,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_funct_1,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc6_xreal_0,cc7_xreal_0,fc11_finseq_1,fc12_membered,fc13_membered,fc23_xreal_0,fc2_membered,fc3_xreal_0,fc4_xreal_0,fc8_xreal_0,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_xreal_0,rc2_funct_1,rc7_finseq_1,rc8_finseq_1,spc5_arithm,spc6_arithm,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k23_binop_2,commutativity_k2_tarski,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k23_binop_2,redefinition_k3_finseq_1,dt_k23_binop_2,dt_k2_relat_1,dt_k2_tarski,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_xcmplx_0,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c2_5_2__jordan2c,dt_c3_5__jordan2c,de_c2_5_2__jordan2c,cc1_xreal_0,fc16_membered,fc2_finset_1,fc3_subset_1,rqLessOrEqual__r1_xreal_0__r2_r1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e1_5__jordan2c,e7_5_2__jordan2c,t27_nat_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqLessOrEqual__r1_xreal_0__r2_r2,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r1]), [interesting(0.5),file(jordan2c,e1_5_2_1__jordan2c),[file(jordan2c,e1_5_2_1__jordan2c)]]). fof(i1_5_2__jordan2c,plain, ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ), inference(percases,[status(thm),assumptions([e1_5_2__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[i1_5_2_1__jordan2c,i2_5_2_1__jordan2c,e1_5_2_1__jordan2c]), [interesting(0.65),file(jordan2c,i1_5_2__jordan2c),[file(jordan2c,i1_5_2__jordan2c)]]). fof(e9_5__jordan2c,plain, ( ( k1_funct_1(c3_5__jordan2c,1) = c2_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ) => ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c]),discharge_asm(discharge,[e1_5_2__jordan2c])],[e1_5_2__jordan2c,i1_5_2__jordan2c]), [interesting(0.8),file(jordan2c,e9_5__jordan2c),[file(jordan2c,e9_5__jordan2c)]]). fof(e2_5__jordan2c,plain,( r2_hidden(1,k2_finseq_1(k3_finseq_1(c3_5__jordan2c))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc12_membered,fc14_membered,fc15_membered,fc2_finseq_1,fc5_membered,fc6_membered,rc1_xreal_0,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc20_membered,cc2_finset_1,cc2_funct_1,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc11_finseq_1,fc13_membered,fc1_finseq_1,fc1_subset_1,fc2_membered,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k2_finseq_1,redefinition_k3_finseq_1,dt_k2_finseq_1,dt_k2_relat_1,dt_k2_tarski,dt_k3_finseq_1,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,cc1_xreal_0,fc16_membered,fc2_finset_1,fc3_subset_1,rqLessOrEqual__r1_xreal_0__r2_r1,t1_subset,t7_boole,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e1_5__jordan2c,t3_finseq_1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r2_r2]), [interesting(0.8),file(jordan2c,e2_5__jordan2c),[file(jordan2c,e2_5__jordan2c)]]). fof(e3_5__jordan2c,plain,( r2_hidden(1,k4_finseq_1(c3_5__jordan2c)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc20_membered,cc2_arytm_3,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_finseq_1,fc6_membered,rc1_arytm_3,rc1_membered,rc1_xreal_0,rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_finseq_1,fc1_subset_1,fc5_membered,rc1_finset_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c3_5__jordan2c,cc1_finseq_1,fc2_membered,rc1_finseq_1,rc1_funct_1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e2_5__jordan2c,d3_finseq_1]), [interesting(0.8),file(jordan2c,e3_5__jordan2c),[file(jordan2c,e3_5__jordan2c)]]). fof(e4_5__jordan2c,plain,( r2_hidden(k1_funct_1(c3_5__jordan2c,1),k2_relat_1(c3_5__jordan2c)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_arytm_3,rc1_xreal_0,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,rc1_finseq_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_finseq_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k4_finseq_1,dt_c3_5__jordan2c,rc1_funct_1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e3_5__jordan2c,d5_funct_1]), [interesting(0.8),file(jordan2c,e4_5__jordan2c),[file(jordan2c,e4_5__jordan2c)]]). fof(e5_5__jordan2c,plain,( r2_hidden(2,k2_finseq_1(k3_finseq_1(c3_5__jordan2c))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc12_membered,fc14_membered,fc15_membered,fc2_finseq_1,fc5_membered,fc6_membered,rc1_xreal_0,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_xreal_0,rc4_xreal_0,rc6_finseq_1,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc20_membered,cc2_finset_1,cc2_funct_1,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc11_finseq_1,fc13_membered,fc1_finseq_1,fc1_subset_1,fc2_membered,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k2_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k2_finseq_1,redefinition_k3_finseq_1,dt_k2_finseq_1,dt_k2_relat_1,dt_k2_tarski,dt_k3_finseq_1,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,cc1_xreal_0,fc16_membered,fc2_finset_1,fc3_subset_1,rqLessOrEqual__r1_xreal_0__r2_r1,t1_subset,t7_boole,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e1_5__jordan2c,t3_finseq_1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r2_r2]), [interesting(0.8),file(jordan2c,e5_5__jordan2c),[file(jordan2c,e5_5__jordan2c)]]). fof(e6_5__jordan2c,plain,( r2_hidden(2,k4_finseq_1(c3_5__jordan2c)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc20_membered,cc2_arytm_3,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc2_finseq_1,fc6_membered,rc1_arytm_3,rc1_membered,rc1_xreal_0,rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_finseq_1,fc1_subset_1,fc5_membered,rc1_finset_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c3_5__jordan2c,cc1_finseq_1,fc2_membered,rc1_finseq_1,rc1_funct_1,t1_subset,t7_boole,spc2_numerals,spc2_boole,e5_5__jordan2c,d3_finseq_1]), [interesting(0.8),file(jordan2c,e6_5__jordan2c),[file(jordan2c,e6_5__jordan2c)]]). fof(e7_5__jordan2c,plain,( r2_hidden(k1_funct_1(c3_5__jordan2c,2),k2_relat_1(c3_5__jordan2c)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_arytm_3,rc1_xreal_0,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,rc1_finseq_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_finseq_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k4_finseq_1,dt_c3_5__jordan2c,rc1_funct_1,t1_subset,t7_boole,spc2_numerals,spc2_boole,e6_5__jordan2c,d5_funct_1]), [interesting(0.8),file(jordan2c,e7_5__jordan2c),[file(jordan2c,e7_5__jordan2c)]]). fof(e1_5_1__jordan2c,assumption, ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c1_5__jordan2c ), introduced(assumption,[file(jordan2c,e1_5_1__jordan2c)]), [interesting(0.65),axiom,file(jordan2c,e1_5_1__jordan2c)]). fof(e1_5_1_1_1__jordan2c,assumption,( c2_5_1__jordan2c = 1 ), introduced(assumption,[file(jordan2c,e1_5_1_1_1__jordan2c)]), [interesting(0.35),axiom,file(jordan2c,e1_5_1_1_1__jordan2c)]). fof(dh_c1_5_1__jordan2c,definition, ( ? [A] : ( r2_hidden(A,k4_finseq_1(c3_5__jordan2c)) & c2_5__jordan2c = k1_funct_1(c3_5__jordan2c,A) ) => ( r2_hidden(c1_5_1__jordan2c,k4_finseq_1(c3_5__jordan2c)) & c2_5__jordan2c = k1_funct_1(c3_5__jordan2c,c1_5_1__jordan2c) ) ), introduced(definition,[new_symbol(c1_5_1__jordan2c),file(jordan2c,c1_5_1__jordan2c)]), [interesting(0.65),axiom,file(jordan2c,c1_5_1__jordan2c)]). fof(e2_5_1__jordan2c,plain,( r2_hidden(c2_5__jordan2c,k2_relat_1(c3_5__jordan2c)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_arytm_3,rc1_xreal_0,rc2_finset_1,rc4_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc11_finseq_1,fc2_membered,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k3_finseq_1,dt_k2_relat_1,dt_k2_tarski,dt_k3_finseq_1,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,fc2_finset_1,fc3_subset_1,t1_subset,t7_boole,spc2_numerals,spc2_boole,e1_5__jordan2c,d2_tarski]), [interesting(0.65),file(jordan2c,e2_5_1__jordan2c),[file(jordan2c,e2_5_1__jordan2c)]]). fof(e3_5_1__jordan2c,plain,( ? [A] : ( r2_hidden(A,k4_finseq_1(c3_5__jordan2c)) & c2_5__jordan2c = k1_funct_1(c3_5__jordan2c,A) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xreal_0,cc7_xreal_0,rc1_arytm_3,rc1_xreal_0,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_numbers,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,fc11_finseq_1,fc17_finseq_1,fc2_finseq_1,fc2_membered,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,redefinition_k5_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc9_membered,fc1_subset_1,rc1_finseq_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_finseq_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k4_finseq_1,dt_c2_5__jordan2c,dt_c3_5__jordan2c,rc1_funct_1,t1_subset,t7_boole,e2_5_1__jordan2c,d5_funct_1]), [interesting(0.65),file(jordan2c,e3_5_1__jordan2c),[file(jordan2c,e3_5_1__jordan2c)]]). fof(dt_c1_5_1__jordan2c,plain,( $true ), inference(consider,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[dh_c1_5_1__jordan2c,e3_5_1__jordan2c]), [interesting(0.65),file(jordan2c,c1_5_1__jordan2c),[file(jordan2c,c1_5_1__jordan2c)]]). fof(de_c2_5_1__jordan2c,definition,( c2_5_1__jordan2c = c1_5_1__jordan2c ), introduced(definition,[new_symbol(c2_5_1__jordan2c),file(jordan2c,c2_5_1__jordan2c)]), [interesting(0.65),axiom,file(jordan2c,c2_5_1__jordan2c)]). fof(e4_5_1__jordan2c,plain, ( r2_hidden(c1_5_1__jordan2c,k4_finseq_1(c3_5__jordan2c)) & c2_5__jordan2c = k1_funct_1(c3_5__jordan2c,c1_5_1__jordan2c) ), inference(consider,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[dh_c1_5_1__jordan2c,e3_5_1__jordan2c]), [interesting(0.65),file(jordan2c,e4_5_1__jordan2c),[file(jordan2c,e4_5_1__jordan2c)]]). fof(e6_5_1__jordan2c,plain,( m2_subset_1(c1_5_1__jordan2c,k1_numbers,k5_numbers) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc17_finseq_1,fc2_finseq_1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc1_xreal_0,rc2_finset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,rc1_finseq_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_5_1__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,fc2_membered,t1_subset,t7_boole,e4_5_1__jordan2c]), [interesting(0.65),file(jordan2c,e6_5_1__jordan2c),[file(jordan2c,e6_5_1__jordan2c)]]). fof(dt_c2_5_1__jordan2c,plain,( m2_subset_1(c2_5_1__jordan2c,k1_numbers,k5_numbers) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc1_finseq_1,cc2_funct_1,cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc1_finseq_1,rc1_funct_1,rc2_finset_1,rc2_funct_1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_finset_1,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc2_finseq_1,fc6_membered,rc1_arytm_3,rc1_finset_1,rc1_membered,rc1_xreal_0,rc3_finset_1,rc4_finset_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc1_subset_1,fc5_membered,rc1_subset_1,rc2_subset_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_m2_subset_1,dt_c1_5_1__jordan2c,fc2_membered,de_c2_5_1__jordan2c,e6_5_1__jordan2c]), [interesting(0.65),file(jordan2c,c2_5_1__jordan2c),[file(jordan2c,c2_5_1__jordan2c)]]). fof(e2_5_1_1_1__jordan2c,plain, ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ), inference(mizar_by,[status(thm),assumptions([e1_5_1_1_1__jordan2c,e1_5_1__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,rc1_arytm_3,rc1_xreal_0,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,fc17_finseq_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,rc1_finseq_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_finseq_1,dt_k1_funct_1,dt_k4_finseq_1,dt_c1_5__jordan2c,dt_c1_5_1__jordan2c,dt_c2_5__jordan2c,dt_c2_5_1__jordan2c,dt_c3_5__jordan2c,de_c2_5_1__jordan2c,t1_subset,t7_boole,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e1_5_1_1_1__jordan2c,e1_5_1__jordan2c,e4_5_1__jordan2c]), [interesting(0.35),file(jordan2c,e2_5_1_1_1__jordan2c),[file(jordan2c,e2_5_1_1_1__jordan2c)]]). fof(i2_5_1_1_1__jordan2c,theorem,( $true ), introduced(tautology,[file(jordan2c,i2_5_1_1_1__jordan2c)]), [interesting(0.35),trivial,file(jordan2c,i2_5_1_1_1__jordan2c)]). fof(i1_5_1_1_1__jordan2c,plain, ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ), inference(conclusion,[status(thm),assumptions([e1_5_1_1_1__jordan2c,e1_5_1__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[e2_5_1_1_1__jordan2c,i2_5_1_1_1__jordan2c]), [interesting(0.35),file(jordan2c,i1_5_1_1_1__jordan2c),[file(jordan2c,i1_5_1_1_1__jordan2c)]]). fof(i1_5_1_1__jordan2c,plain, ( c2_5_1__jordan2c = 1 => ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ) ), inference(discharge_asm,[status(thm),assumptions([e1_5_1__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c]),discharge_asm(discharge,[e1_5_1_1_1__jordan2c])],[e1_5_1_1_1__jordan2c,i1_5_1_1_1__jordan2c]), [interesting(0.5),file(jordan2c,i1_5_1_1__jordan2c),[file(jordan2c,i1_5_1_1__jordan2c)]]). fof(e1_5_1_1_2__jordan2c,assumption,( c2_5_1__jordan2c = k23_binop_2(1,1) ), introduced(assumption,[file(jordan2c,e1_5_1_1_2__jordan2c)]), [interesting(0.35),axiom,file(jordan2c,e1_5_1_1_2__jordan2c)]). fof(e2_5_1_1_2__jordan2c,plain, ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ), inference(mizar_by,[status(thm),assumptions([e1_5_1_1_2__jordan2c,e1_5_1__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc7_xreal_0,fc9_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc23_xreal_0,fc3_xreal_0,fc4_xreal_0,fc8_xreal_0,rc1_arytm_3,rc1_xreal_0,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,fc17_finseq_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc6_membered,cc9_membered,fc1_subset_1,fc2_membered,rc1_finseq_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,spc5_arithm,spc6_arithm,spc7_arithm,t2_subset,t3_arithm,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k23_binop_2,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,antisymmetry_r2_hidden,redefinition_k23_binop_2,redefinition_k4_finseq_1,dt_k1_funct_1,dt_k23_binop_2,dt_k2_xcmplx_0,dt_k3_xcmplx_0,dt_k4_finseq_1,dt_c1_5__jordan2c,dt_c1_5_1__jordan2c,dt_c2_5__jordan2c,dt_c2_5_1__jordan2c,dt_c3_5__jordan2c,de_c2_5_1__jordan2c,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,t1_subset,t7_boole,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e1_5_1_1_2__jordan2c,e1_5_1__jordan2c,e4_5_1__jordan2c,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2]), [interesting(0.35),file(jordan2c,e2_5_1_1_2__jordan2c),[file(jordan2c,e2_5_1_1_2__jordan2c)]]). fof(i2_5_1_1_2__jordan2c,theorem,( $true ), introduced(tautology,[file(jordan2c,i2_5_1_1_2__jordan2c)]), [interesting(0.35),trivial,file(jordan2c,i2_5_1_1_2__jordan2c)]). fof(i1_5_1_1_2__jordan2c,plain, ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ), inference(conclusion,[status(thm),assumptions([e1_5_1_1_2__jordan2c,e1_5_1__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[e2_5_1_1_2__jordan2c,i2_5_1_1_2__jordan2c]), [interesting(0.35),file(jordan2c,i1_5_1_1_2__jordan2c),[file(jordan2c,i1_5_1_1_2__jordan2c)]]). fof(i2_5_1_1__jordan2c,plain, ( c2_5_1__jordan2c = k23_binop_2(1,1) => ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ) ), inference(discharge_asm,[status(thm),assumptions([e1_5_1__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c]),discharge_asm(discharge,[e1_5_1_1_2__jordan2c])],[e1_5_1_1_2__jordan2c,i1_5_1_1_2__jordan2c]), [interesting(0.5),file(jordan2c,i2_5_1_1__jordan2c),[file(jordan2c,i2_5_1_1__jordan2c)]]). fof(e5_5_1__jordan2c,plain,( r2_hidden(c1_5_1__jordan2c,k2_finseq_1(k3_finseq_1(c3_5__jordan2c))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc3_xreal_0,cc4_xreal_0,cc5_xreal_0,cc6_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc20_membered,cc2_arytm_3,cc2_membered,cc2_xreal_0,cc3_membered,cc7_xreal_0,fc2_finseq_1,fc6_membered,rc1_arytm_3,rc1_membered,rc1_xreal_0,rc2_finset_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,existence_m1_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finset_1,cc1_funct_1,cc1_xreal_0,cc2_finset_1,cc2_funct_1,cc3_arytm_3,cc4_membered,cc6_membered,cc9_membered,fc17_finseq_1,fc1_finseq_1,fc1_subset_1,fc5_membered,rc1_finset_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,rc3_finset_1,rc4_finset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_subset_1,redefinition_k2_finseq_1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k1_relat_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_numbers,dt_m2_subset_1,dt_c1_5_1__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,cc1_finseq_1,fc2_membered,rc1_finseq_1,rc1_funct_1,t1_subset,t7_boole,e4_5_1__jordan2c,d3_finseq_1]), [interesting(0.65),file(jordan2c,e5_5_1__jordan2c),[file(jordan2c,e5_5_1__jordan2c)]]). fof(e7_5_1__jordan2c,plain, ( r1_xreal_0(1,c2_5_1__jordan2c) & r1_xreal_0(c2_5_1__jordan2c,k3_finseq_1(c3_5__jordan2c)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc2_finseq_1,fc5_membered,fc6_membered,rc1_finset_1,rc1_membered,rc1_xreal_0,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc2_xreal_0,cc3_xreal_0,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc1_finseq_1,fc1_subset_1,fc2_membered,rc1_finseq_1,rc1_funct_1,rc1_subset_1,rc2_funct_1,rc2_subset_1,t1_real,t2_subset,t3_subset,t4_real,t4_subset,t5_subset,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k2_finseq_1,redefinition_k3_finseq_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_c1_5_1__jordan2c,dt_c2_5_1__jordan2c,dt_c3_5__jordan2c,de_c2_5_1__jordan2c,cc1_xreal_0,rqLessOrEqual__r1_xreal_0__r1_r1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e5_5_1__jordan2c,t3_finseq_1]), [interesting(0.65),file(jordan2c,e7_5_1__jordan2c),[file(jordan2c,e7_5_1__jordan2c)]]). fof(e1_5_1_1__jordan2c,plain, ( c2_5_1__jordan2c = 1 | c2_5_1__jordan2c = k23_binop_2(1,1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[reflexivity_r1_tarski,cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,rc2_finset_1,rc4_funct_1,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc20_membered,cc2_finset_1,cc3_arytm_3,cc4_xreal_0,cc5_xreal_0,cc6_membered,cc8_xreal_0,cc9_membered,fc10_xreal_0,fc11_xreal_0,fc12_xreal_0,fc14_membered,fc15_membered,fc1_subset_1,fc21_xreal_0,fc22_xreal_0,fc24_xreal_0,fc2_finseq_1,fc5_membered,fc6_membered,fc7_xreal_0,fc9_xreal_0,rc1_subset_1,rc2_subset_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_xreal_0,rc4_finset_1,rc4_xreal_0,rc6_finseq_1,t1_subset,t2_real,t3_real,t3_subset,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,dt_c1_5_1__jordan2c,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc1_membered,cc2_funct_1,cc2_membered,cc2_xreal_0,cc3_membered,cc3_xreal_0,cc4_membered,cc6_xreal_0,cc7_xreal_0,fc11_finseq_1,fc12_membered,fc13_membered,fc23_xreal_0,fc2_membered,fc3_xreal_0,fc4_xreal_0,fc8_xreal_0,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_membered,rc1_xreal_0,rc2_funct_1,rc7_finseq_1,rc8_finseq_1,spc5_arithm,spc6_arithm,spc7_arithm,t1_real,t2_subset,t3_arithm,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k23_binop_2,commutativity_k2_tarski,commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k23_binop_2,redefinition_k3_finseq_1,dt_k23_binop_2,dt_k2_relat_1,dt_k2_tarski,dt_k2_xcmplx_0,dt_k3_finseq_1,dt_k3_xcmplx_0,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c2_5_1__jordan2c,dt_c3_5__jordan2c,de_c2_5_1__jordan2c,cc1_xreal_0,fc16_membered,fc2_finset_1,fc3_subset_1,rqLessOrEqual__r1_xreal_0__r2_r1,rqRealMult__k3_xcmplx_0__r1_r1_r1,rqRealMult__k3_xcmplx_0__r1_r2_r2,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e1_5__jordan2c,e7_5_1__jordan2c,t27_nat_1,rqRealAdd__k2_xcmplx_0__r1_r1_r2,rqRealMult__k3_xcmplx_0__r2_r1_r2,rqLessOrEqual__r1_xreal_0__r2_r2,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r1]), [interesting(0.5),file(jordan2c,e1_5_1_1__jordan2c),[file(jordan2c,e1_5_1_1__jordan2c)]]). fof(i1_5_1__jordan2c,plain, ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ), inference(percases,[status(thm),assumptions([e1_5_1__jordan2c,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[i1_5_1_1__jordan2c,i2_5_1_1__jordan2c,e1_5_1_1__jordan2c]), [interesting(0.65),file(jordan2c,i1_5_1__jordan2c),[file(jordan2c,i1_5_1__jordan2c)]]). fof(e8_5__jordan2c,plain, ( ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c1_5__jordan2c ) => ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c]),discharge_asm(discharge,[e1_5_1__jordan2c])],[e1_5_1__jordan2c,i1_5_1__jordan2c]), [interesting(0.8),file(jordan2c,e8_5__jordan2c),[file(jordan2c,e8_5__jordan2c)]]). fof(e10_5__jordan2c,plain,( ~ ( ~ ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ) & ~ ( k1_funct_1(c3_5__jordan2c,1) = c2_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c1_5__jordan2c ) ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,rc2_xreal_0,rc3_xreal_0,rc4_xreal_0,reflexivity_r1_tarski,cc1_arytm_3,cc1_xreal_0,cc2_arytm_3,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_arytm_3,rc1_xreal_0,rc2_finset_1,rc4_funct_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_finset_1,cc2_membered,cc3_arytm_3,cc3_membered,cc4_membered,cc6_membered,cc9_membered,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc2_subset_1,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc4_finset_1,rc6_finseq_1,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_funct_1,fc11_finseq_1,fc2_membered,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc2_funct_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t6_boole,t8_boole,commutativity_k2_tarski,antisymmetry_r2_hidden,redefinition_k3_finseq_1,dt_k1_funct_1,dt_k2_relat_1,dt_k2_tarski,dt_k3_finseq_1,dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,fc2_finset_1,fc3_subset_1,t1_subset,t7_boole,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e9_5__jordan2c,e1_5__jordan2c,e4_5__jordan2c,e7_5__jordan2c,e8_5__jordan2c,d2_tarski]), [interesting(0.8),file(jordan2c,e10_5__jordan2c),[file(jordan2c,e10_5__jordan2c)]]). fof(i5_5__jordan2c,theorem,( $true ), introduced(tautology,[file(jordan2c,i5_5__jordan2c)]), [interesting(0.8),trivial,file(jordan2c,i5_5__jordan2c)]). fof(i4_5__jordan2c,plain,( ~ ( ~ ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ) & ~ ( k1_funct_1(c3_5__jordan2c,1) = c2_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c1_5__jordan2c ) ) ), inference(conclusion,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c,e1_5__jordan2c])],[e10_5__jordan2c,i5_5__jordan2c]), [interesting(0.8),file(jordan2c,i4_5__jordan2c),[file(jordan2c,i4_5__jordan2c)]]). fof(i3_5__jordan2c,plain,( ~ ( k2_relat_1(c3_5__jordan2c) = k2_tarski(c1_5__jordan2c,c2_5__jordan2c) & k3_finseq_1(c3_5__jordan2c) = 2 & ~ ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ) & ~ ( k1_funct_1(c3_5__jordan2c,1) = c2_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c1_5__jordan2c ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c,dt_c3_5__jordan2c]),discharge_asm(discharge,[e1_5__jordan2c])],[e1_5__jordan2c,i4_5__jordan2c]), [interesting(0.8),file(jordan2c,i3_5__jordan2c),[file(jordan2c,i3_5__jordan2c)]]). fof(i3_5_tmp__jordan2c,plain, ( ( v1_relat_1(c3_5__jordan2c) & v1_funct_1(c3_5__jordan2c) & v1_finseq_1(c3_5__jordan2c) ) => ~ ( k2_relat_1(c3_5__jordan2c) = k2_tarski(c1_5__jordan2c,c2_5__jordan2c) & k3_finseq_1(c3_5__jordan2c) = 2 & ~ ( k1_funct_1(c3_5__jordan2c,1) = c1_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c2_5__jordan2c ) & ~ ( k1_funct_1(c3_5__jordan2c,1) = c2_5__jordan2c & k1_funct_1(c3_5__jordan2c,2) = c1_5__jordan2c ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c]),discharge_asm(discharge,[dt_c3_5__jordan2c])],[dt_c3_5__jordan2c,i3_5__jordan2c]), [interesting(0.8),i2_5__jordan2c]). fof(i2_5__jordan2c,plain,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ~ ( k2_relat_1(A) = k2_tarski(c1_5__jordan2c,c2_5__jordan2c) & k3_finseq_1(A) = 2 & ~ ( k1_funct_1(A,1) = c1_5__jordan2c & k1_funct_1(A,2) = c2_5__jordan2c ) & ~ ( k1_funct_1(A,1) = c2_5__jordan2c & k1_funct_1(A,2) = c1_5__jordan2c ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_5__jordan2c,dt_c2_5__jordan2c])],[i3_5_tmp__jordan2c,dh_c3_5__jordan2c]), [interesting(0.8),file(jordan2c,i2_5__jordan2c),[file(jordan2c,i2_5__jordan2c)]]). fof(i2_5_tmp__jordan2c,plain,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ~ ( k2_relat_1(A) = k2_tarski(c1_5__jordan2c,c2_5__jordan2c) & k3_finseq_1(A) = 2 & ~ ( k1_funct_1(A,1) = c1_5__jordan2c & k1_funct_1(A,2) = c2_5__jordan2c ) & ~ ( k1_funct_1(A,1) = c2_5__jordan2c & k1_funct_1(A,2) = c1_5__jordan2c ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_5__jordan2c]),discharge_asm(discharge,[dt_c2_5__jordan2c])],[dt_c2_5__jordan2c,i2_5__jordan2c]), [interesting(0.8),i1_5__jordan2c]). fof(i1_5__jordan2c,plain,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( k2_relat_1(B) = k2_tarski(c1_5__jordan2c,A) & k3_finseq_1(B) = 2 & ~ ( k1_funct_1(B,1) = c1_5__jordan2c & k1_funct_1(B,2) = A ) & ~ ( k1_funct_1(B,1) = A & k1_funct_1(B,2) = c1_5__jordan2c ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_5__jordan2c])],[i2_5_tmp__jordan2c,dh_c2_5__jordan2c]), [interesting(0.8),file(jordan2c,i1_5__jordan2c),[file(jordan2c,i1_5__jordan2c)]]). fof(i1_5_tmp__jordan2c,plain,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( k2_relat_1(B) = k2_tarski(c1_5__jordan2c,A) & k3_finseq_1(B) = 2 & ~ ( k1_funct_1(B,1) = c1_5__jordan2c & k1_funct_1(B,2) = A ) & ~ ( k1_funct_1(B,1) = A & k1_funct_1(B,2) = c1_5__jordan2c ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_5__jordan2c])],[dt_c1_5__jordan2c,i1_5__jordan2c]), [interesting(1),t7_jordan2c]). fof(t7_jordan2c,theorem,( ! [A,B,C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( k2_relat_1(C) = k2_tarski(A,B) & k3_finseq_1(C) = 2 & ~ ( k1_funct_1(C,1) = A & k1_funct_1(C,2) = B ) & ~ ( k1_funct_1(C,1) = B & k1_funct_1(C,2) = A ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_5_tmp__jordan2c,dh_c1_5__jordan2c]), [interesting(1),file(jordan2c,t7_jordan2c),[file(jordan2c,t7_jordan2c)]]).