% Mizar ND problem: t8_jordan2c,jordan2c,153,16 fof(dh_c1_6__jordan2c,definition, ( ( m1_subset_1(c1_6__jordan2c,k1_numbers) => ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( ( v1_goboard1(B) & m2_finseq_1(B,k1_numbers) ) => ( ( k2_relat_1(B) = k2_tarski(c1_6__jordan2c,A) & k3_finseq_1(B) = 2 & r1_xreal_0(c1_6__jordan2c,A) ) => ( k1_goboard1(B,1) = c1_6__jordan2c & k1_goboard1(B,2) = A ) ) ) ) ) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( ( v1_goboard1(E) & m2_finseq_1(E,k1_numbers) ) => ( ( k2_relat_1(E) = k2_tarski(C,D) & k3_finseq_1(E) = 2 & r1_xreal_0(C,D) ) => ( k1_goboard1(E,1) = C & k1_goboard1(E,2) = D ) ) ) ) ) ), introduced(definition,[new_symbol(c1_6__jordan2c),file(jordan2c,c1_6__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,c1_6__jordan2c)]). fof(dh_c2_6__jordan2c,definition, ( ( m1_subset_1(c2_6__jordan2c,k1_numbers) => ! [A] : ( ( v1_goboard1(A) & m2_finseq_1(A,k1_numbers) ) => ( ( k2_relat_1(A) = k2_tarski(c1_6__jordan2c,c2_6__jordan2c) & k3_finseq_1(A) = 2 & r1_xreal_0(c1_6__jordan2c,c2_6__jordan2c) ) => ( k1_goboard1(A,1) = c1_6__jordan2c & k1_goboard1(A,2) = c2_6__jordan2c ) ) ) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( ( v1_goboard1(C) & m2_finseq_1(C,k1_numbers) ) => ( ( k2_relat_1(C) = k2_tarski(c1_6__jordan2c,B) & k3_finseq_1(C) = 2 & r1_xreal_0(c1_6__jordan2c,B) ) => ( k1_goboard1(C,1) = c1_6__jordan2c & k1_goboard1(C,2) = B ) ) ) ) ), introduced(definition,[new_symbol(c2_6__jordan2c),file(jordan2c,c2_6__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,c2_6__jordan2c)]). fof(dh_c3_6__jordan2c,definition, ( ( ( v1_goboard1(c3_6__jordan2c) & m2_finseq_1(c3_6__jordan2c,k1_numbers) ) => ( ( k2_relat_1(c3_6__jordan2c) = k2_tarski(c1_6__jordan2c,c2_6__jordan2c) & k3_finseq_1(c3_6__jordan2c) = 2 & r1_xreal_0(c1_6__jordan2c,c2_6__jordan2c) ) => ( k1_goboard1(c3_6__jordan2c,1) = c1_6__jordan2c & k1_goboard1(c3_6__jordan2c,2) = c2_6__jordan2c ) ) ) => ! [A] : ( ( v1_goboard1(A) & m2_finseq_1(A,k1_numbers) ) => ( ( k2_relat_1(A) = k2_tarski(c1_6__jordan2c,c2_6__jordan2c) & k3_finseq_1(A) = 2 & r1_xreal_0(c1_6__jordan2c,c2_6__jordan2c) ) => ( k1_goboard1(A,1) = c1_6__jordan2c & k1_goboard1(A,2) = c2_6__jordan2c ) ) ) ), introduced(definition,[new_symbol(c3_6__jordan2c),file(jordan2c,c3_6__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,c3_6__jordan2c)]). fof(e1_6__jordan2c,assumption, ( k2_relat_1(c3_6__jordan2c) = k2_tarski(c1_6__jordan2c,c2_6__jordan2c) & k3_finseq_1(c3_6__jordan2c) = 2 & r1_xreal_0(c1_6__jordan2c,c2_6__jordan2c) ), introduced(assumption,[file(jordan2c,e1_6__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,e1_6__jordan2c)]). fof(reflexivity_r1_tarski,theorem,( ! [A,B] : r1_tarski(A,A) ), file(tarski,r1_tarski), [interesting(0.9),axiom,file(tarski,r1_tarski)]). fof(existence_m1_relset_1,axiom,( ! [A,B] : ? [C] : m1_relset_1(C,A,B) ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). fof(dt_k2_zfmisc_1,axiom,( $true ), file(zfmisc_1,k2_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_1)]). 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_relset_1,theorem,( ! [A,B,C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) ), file(relset_1,cc1_relset_1), [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]). 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(fc14_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) ), file(finset_1,fc14_finset_1), [interesting(0.9),axiom,file(finset_1,fc14_finset_1)]). 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(fc4_subset_1,theorem,( ! [A,B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ), file(subset_1,fc4_subset_1), [interesting(0.9),axiom,file(subset_1,fc4_subset_1)]). 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(rc2_finseq_1,theorem,( ! [A] : ? [B] : ( m1_relset_1(B,k5_numbers,A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc2_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc2_finseq_1)]). 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(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(existence_m2_relset_1,axiom,( ! [A,B] : ? [C] : m2_relset_1(C,A,B) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). fof(redefinition_m2_relset_1,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) <=> m1_relset_1(C,A,B) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_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(dt_m2_relset_1,axiom,( ! [A,B,C] : ( m2_relset_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ), file(relset_1,m2_relset_1), [interesting(0.9),axiom,file(relset_1,m2_relset_1)]). 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(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(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(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(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(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(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(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_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(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_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(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_finseq_1,theorem,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ), file(finseq_1,rc4_finseq_1), [interesting(0.9),axiom,file(finseq_1,rc4_finseq_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(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(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(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(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(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_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(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(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(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). 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_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_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_finseq_1,definition,( ! [A,B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]). 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_finseq_1,axiom,( ! [A,B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ), file(finseq_1,m1_finseq_1), [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]). 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_finseq_1,axiom,( ! [A,B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m2_relset_1(B,k5_numbers,A) ) ) ), file(finseq_1,m2_finseq_1), [interesting(0.9),axiom,file(finseq_1,m2_finseq_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_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(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(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(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(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_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_goboard1,theorem,( ? [A] : ( m1_finseq_1(A,k1_numbers) & ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v1_goboard1(A) ) ), file(goboard1,rc1_goboard1), [interesting(0.9),axiom,file(goboard1,rc1_goboard1)]). 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(rc2_goboard1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) ) ) ), file(goboard1,rc2_goboard1), [interesting(0.9),axiom,file(goboard1,rc2_goboard1)]). 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(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(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(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(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(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(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(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(redefinition_k1_goboard1,definition,( ! [A,B] : ( ( m1_finseq_1(A,k1_numbers) & m1_subset_1(B,k5_numbers) ) => k1_goboard1(A,B) = k1_funct_1(A,B) ) ), file(goboard1,k1_goboard1), [interesting(0.9),axiom,file(goboard1,k1_goboard1)]). 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_k1_goboard1,axiom,( ! [A,B] : ( ( m1_finseq_1(A,k1_numbers) & m1_subset_1(B,k5_numbers) ) => m1_subset_1(k1_goboard1(A,B),k1_numbers) ) ), file(goboard1,k1_goboard1), [interesting(0.9),axiom,file(goboard1,k1_goboard1)]). 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_6__jordan2c,assumption,( m1_subset_1(c1_6__jordan2c,k1_numbers) ), introduced(assumption,[file(jordan2c,c1_6__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,c1_6__jordan2c)]). fof(dt_c2_6__jordan2c,assumption,( m1_subset_1(c2_6__jordan2c,k1_numbers) ), introduced(assumption,[file(jordan2c,c2_6__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,c2_6__jordan2c)]). fof(dt_c3_6__jordan2c,assumption, ( v1_goboard1(c3_6__jordan2c) & m2_finseq_1(c3_6__jordan2c,k1_numbers) ), introduced(assumption,[file(jordan2c,c3_6__jordan2c)]), [interesting(0.8),axiom,file(jordan2c,c3_6__jordan2c)]). 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(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(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_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(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(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(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(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(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_6_1__jordan2c,assumption, ( k1_goboard1(c3_6__jordan2c,1) = c2_6__jordan2c & k1_goboard1(c3_6__jordan2c,2) = c1_6__jordan2c ), introduced(assumption,[file(jordan2c,e1_6_1__jordan2c)]), [interesting(0.65),axiom,file(jordan2c,e1_6_1__jordan2c)]). fof(dt_k1_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). 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(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(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(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(e4_6_1__jordan2c,plain,( r2_hidden(2,k2_finseq_1(k3_finseq_1(c3_6__jordan2c))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__jordan2c,e1_6__jordan2c])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_arytm_3,cc1_relset_1,cc2_arytm_3,fc14_finset_1,fc4_subset_1,rc1_arytm_3,rc2_finseq_1,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,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_goboard1,rc1_xreal_0,rc2_goboard1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,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_finseq_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_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__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_6__jordan2c,t3_finseq_1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r2_r2]), [interesting(0.65),file(jordan2c,e4_6_1__jordan2c),[file(jordan2c,e4_6_1__jordan2c)]]). 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_6_1__jordan2c,plain,( r2_hidden(2,k4_finseq_1(c3_6__jordan2c)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__jordan2c,e1_6__jordan2c])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_xreal_0,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m2_relset_1,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_goboard1,rc1_membered,rc1_xreal_0,rc2_finset_1,rc2_goboard1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_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_6__jordan2c,cc1_finseq_1,fc2_membered,rc1_finseq_1,rc1_funct_1,t1_subset,t7_boole,spc2_numerals,spc2_boole,e4_6_1__jordan2c,d3_finseq_1]), [interesting(0.65),file(jordan2c,e5_6_1__jordan2c),[file(jordan2c,e5_6_1__jordan2c)]]). fof(e2_6_1__jordan2c,plain,( r2_hidden(1,k2_finseq_1(k3_finseq_1(c3_6__jordan2c))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__jordan2c,e1_6__jordan2c])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_arytm_3,cc1_relset_1,cc2_arytm_3,fc14_finset_1,fc4_subset_1,rc1_arytm_3,rc2_finseq_1,rc2_finset_1,rc4_funct_1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_ordinal2,dt_m1_finseq_1,dt_m2_relset_1,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_goboard1,rc1_xreal_0,rc2_goboard1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,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_finseq_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_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__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_6__jordan2c,t3_finseq_1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r2_r2]), [interesting(0.65),file(jordan2c,e2_6_1__jordan2c),[file(jordan2c,e2_6_1__jordan2c)]]). fof(e3_6_1__jordan2c,plain,( r2_hidden(1,k4_finseq_1(c3_6__jordan2c)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__jordan2c,e1_6__jordan2c])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc14_finset_1,fc4_subset_1,rc2_finseq_1,rc2_xreal_0,rc3_xreal_0,rc4_funct_1,rc4_xreal_0,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m2_relset_1,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_goboard1,rc1_membered,rc1_xreal_0,rc2_finset_1,rc2_goboard1,rc3_finseq_1,rc3_funct_1,rc4_finseq_1,rc6_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_subset_1,dt_m2_finseq_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_6__jordan2c,cc1_finseq_1,fc2_membered,rc1_finseq_1,rc1_funct_1,t1_subset,t7_boole,spc1_numerals,spc1_boole,e2_6_1__jordan2c,d3_finseq_1]), [interesting(0.65),file(jordan2c,e3_6_1__jordan2c),[file(jordan2c,e3_6_1__jordan2c)]]). fof(d1_goboard1,definition,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( v1_goboard1(A) <=> ! [B] : ( m2_subset_1(B,k1_numbers,k5_numbers) => ! [C] : ( m2_subset_1(C,k1_numbers,k5_numbers) => ~ ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) & ~ r1_xreal_0(C,B) & r1_xreal_0(k1_goboard1(A,C),k1_goboard1(A,B)) ) ) ) ) ) ), file(goboard1,d1_goboard1), [interesting(0.9),axiom,file(goboard1,d1_goboard1)]). fof(e6_6_1__jordan2c,plain, ( k1_goboard1(c3_6__jordan2c,1) = c1_6__jordan2c & k1_goboard1(c3_6__jordan2c,2) = c2_6__jordan2c ), inference(mizar_by,[status(thm),assumptions([e1_6_1__jordan2c,dt_c1_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__jordan2c,e1_6__jordan2c])],[fc14_membered,fc15_membered,rc4_funct_1,reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_arytm_3,cc1_membered,cc1_relset_1,cc1_xreal_0,cc20_membered,cc2_arytm_3,cc2_membered,cc3_membered,cc4_xreal_0,cc5_xreal_0,cc8_xreal_0,fc12_membered,fc14_finset_1,fc16_membered,fc2_finseq_1,fc4_subset_1,fc6_membered,rc1_arytm_3,rc1_membered,rc1_xreal_0,rc2_finseq_1,rc2_finset_1,rc2_xreal_0,rc3_finseq_1,rc3_funct_1,rc3_xreal_0,rc4_finseq_1,rc4_xreal_0,rc6_finseq_1,t2_real,t3_real,t5_real,t6_real,t7_real,t8_real,existence_m1_finseq_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_funct_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_finseq_1,cc1_finset_1,cc1_funct_1,cc2_finset_1,cc2_funct_1,cc2_xreal_0,cc3_arytm_3,cc3_xreal_0,cc4_membered,cc6_membered,cc6_xreal_0,cc7_xreal_0,cc9_membered,fc11_finseq_1,fc13_membered,fc17_finseq_1,fc1_subset_1,fc5_membered,rc1_finseq_1,rc1_finset_1,rc1_funct_1,rc1_goboard1,rc1_subset_1,rc2_funct_1,rc2_goboard1,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,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k1_goboard1,redefinition_k3_finseq_1,redefinition_k4_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_goboard1,dt_k1_numbers,dt_k2_relat_1,dt_k2_tarski,dt_k3_finseq_1,dt_k4_finseq_1,dt_k5_numbers,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__jordan2c,fc2_finset_1,fc2_membered,fc3_subset_1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r2_r2,t1_subset,t7_boole,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e5_6_1__jordan2c,e1_6__jordan2c,e1_6_1__jordan2c,e3_6_1__jordan2c,d1_goboard1,rqLessOrEqual__r1_xreal_0__r2_r1]), [interesting(0.65),file(jordan2c,e6_6_1__jordan2c),[file(jordan2c,e6_6_1__jordan2c)]]). fof(i2_6_1__jordan2c,theorem,( $true ), introduced(tautology,[file(jordan2c,i2_6_1__jordan2c)]), [interesting(0.65),trivial,file(jordan2c,i2_6_1__jordan2c)]). fof(i1_6_1__jordan2c,plain, ( k1_goboard1(c3_6__jordan2c,1) = c1_6__jordan2c & k1_goboard1(c3_6__jordan2c,2) = c2_6__jordan2c ), inference(conclusion,[status(thm),assumptions([e1_6_1__jordan2c,dt_c1_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__jordan2c,e1_6__jordan2c])],[e6_6_1__jordan2c,i2_6_1__jordan2c]), [interesting(0.65),file(jordan2c,i1_6_1__jordan2c),[file(jordan2c,i1_6_1__jordan2c)]]). fof(e2_6__jordan2c,plain, ( ( k1_goboard1(c3_6__jordan2c,1) = c2_6__jordan2c & k1_goboard1(c3_6__jordan2c,2) = c1_6__jordan2c ) => ( k1_goboard1(c3_6__jordan2c,1) = c1_6__jordan2c & k1_goboard1(c3_6__jordan2c,2) = c2_6__jordan2c ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__jordan2c,e1_6__jordan2c]),discharge_asm(discharge,[e1_6_1__jordan2c])],[e1_6_1__jordan2c,i1_6_1__jordan2c]), [interesting(0.8),file(jordan2c,e2_6__jordan2c),[file(jordan2c,e2_6__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 ) ) ) ), file(jordan2c,t7_jordan2c), [interesting(0.9),axiom,file(jordan2c,t7_jordan2c)]). fof(e3_6__jordan2c,plain, ( k1_goboard1(c3_6__jordan2c,1) = c1_6__jordan2c & k1_goboard1(c3_6__jordan2c,2) = c2_6__jordan2c ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__jordan2c,e1_6__jordan2c])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_arytm_3,cc1_relset_1,cc1_xreal_0,cc2_arytm_3,fc14_finset_1,fc14_membered,fc15_membered,fc16_membered,fc4_subset_1,rc1_arytm_3,rc2_finseq_1,rc2_finset_1,rc4_funct_1,antisymmetry_r2_hidden,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m2_relset_1,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,cc6_membered,cc8_xreal_0,cc9_membered,fc12_membered,fc1_subset_1,fc2_finseq_1,fc5_membered,fc6_membered,rc1_membered,rc1_subset_1,rc1_xreal_0,rc2_subset_1,rc2_xreal_0,rc3_finseq_1,rc3_finset_1,rc3_funct_1,rc3_xreal_0,rc4_finseq_1,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_finseq_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_numbers,dt_k5_numbers,dt_m1_finseq_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_subset_1,cc15_membered,cc1_finset_1,cc1_funct_1,cc2_funct_1,cc2_xreal_0,cc3_xreal_0,cc6_xreal_0,cc7_xreal_0,fc11_finseq_1,fc13_membered,fc2_membered,rc1_finset_1,rc1_goboard1,rc2_funct_1,rc2_goboard1,rc7_finseq_1,rc8_finseq_1,t1_real,t2_subset,t4_real,t6_boole,t7_boole,t8_boole,commutativity_k2_tarski,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,redefinition_k1_goboard1,redefinition_k3_finseq_1,dt_k1_funct_1,dt_k1_goboard1,dt_k2_relat_1,dt_k2_tarski,dt_k3_finseq_1,dt_c1_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__jordan2c,cc1_finseq_1,fc2_finset_1,fc3_subset_1,rc1_finseq_1,rc1_funct_1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r1_r2,rqLessOrEqual__r1_xreal_0__r2_r1,rqLessOrEqual__r1_xreal_0__r2_r2,spc1_numerals,spc2_numerals,spc1_boole,spc2_boole,e2_6__jordan2c,e1_6__jordan2c,t7_jordan2c]), [interesting(0.8),file(jordan2c,e3_6__jordan2c),[file(jordan2c,e3_6__jordan2c)]]). fof(i5_6__jordan2c,theorem,( $true ), introduced(tautology,[file(jordan2c,i5_6__jordan2c)]), [interesting(0.8),trivial,file(jordan2c,i5_6__jordan2c)]). fof(i4_6__jordan2c,plain, ( k1_goboard1(c3_6__jordan2c,1) = c1_6__jordan2c & k1_goboard1(c3_6__jordan2c,2) = c2_6__jordan2c ), inference(conclusion,[status(thm),assumptions([dt_c1_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__jordan2c,e1_6__jordan2c])],[e3_6__jordan2c,i5_6__jordan2c]), [interesting(0.8),file(jordan2c,i4_6__jordan2c),[file(jordan2c,i4_6__jordan2c)]]). fof(i3_6__jordan2c,plain, ( ( k2_relat_1(c3_6__jordan2c) = k2_tarski(c1_6__jordan2c,c2_6__jordan2c) & k3_finseq_1(c3_6__jordan2c) = 2 & r1_xreal_0(c1_6__jordan2c,c2_6__jordan2c) ) => ( k1_goboard1(c3_6__jordan2c,1) = c1_6__jordan2c & k1_goboard1(c3_6__jordan2c,2) = c2_6__jordan2c ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__jordan2c,dt_c2_6__jordan2c,dt_c3_6__jordan2c]),discharge_asm(discharge,[e1_6__jordan2c])],[e1_6__jordan2c,i4_6__jordan2c]), [interesting(0.8),file(jordan2c,i3_6__jordan2c),[file(jordan2c,i3_6__jordan2c)]]). fof(i3_6_tmp__jordan2c,plain, ( ( v1_goboard1(c3_6__jordan2c) & m2_finseq_1(c3_6__jordan2c,k1_numbers) ) => ( ( k2_relat_1(c3_6__jordan2c) = k2_tarski(c1_6__jordan2c,c2_6__jordan2c) & k3_finseq_1(c3_6__jordan2c) = 2 & r1_xreal_0(c1_6__jordan2c,c2_6__jordan2c) ) => ( k1_goboard1(c3_6__jordan2c,1) = c1_6__jordan2c & k1_goboard1(c3_6__jordan2c,2) = c2_6__jordan2c ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__jordan2c,dt_c2_6__jordan2c]),discharge_asm(discharge,[dt_c3_6__jordan2c])],[dt_c3_6__jordan2c,i3_6__jordan2c]), [interesting(0.8),i2_6__jordan2c]). fof(i2_6__jordan2c,plain,( ! [A] : ( ( v1_goboard1(A) & m2_finseq_1(A,k1_numbers) ) => ( ( k2_relat_1(A) = k2_tarski(c1_6__jordan2c,c2_6__jordan2c) & k3_finseq_1(A) = 2 & r1_xreal_0(c1_6__jordan2c,c2_6__jordan2c) ) => ( k1_goboard1(A,1) = c1_6__jordan2c & k1_goboard1(A,2) = c2_6__jordan2c ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__jordan2c,dt_c2_6__jordan2c])],[i3_6_tmp__jordan2c,dh_c3_6__jordan2c]), [interesting(0.8),file(jordan2c,i2_6__jordan2c),[file(jordan2c,i2_6__jordan2c)]]). fof(i2_6_tmp__jordan2c,plain, ( m1_subset_1(c2_6__jordan2c,k1_numbers) => ! [A] : ( ( v1_goboard1(A) & m2_finseq_1(A,k1_numbers) ) => ( ( k2_relat_1(A) = k2_tarski(c1_6__jordan2c,c2_6__jordan2c) & k3_finseq_1(A) = 2 & r1_xreal_0(c1_6__jordan2c,c2_6__jordan2c) ) => ( k1_goboard1(A,1) = c1_6__jordan2c & k1_goboard1(A,2) = c2_6__jordan2c ) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__jordan2c]),discharge_asm(discharge,[dt_c2_6__jordan2c])],[dt_c2_6__jordan2c,i2_6__jordan2c]), [interesting(0.8),i1_6__jordan2c]). fof(i1_6__jordan2c,plain,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( ( v1_goboard1(B) & m2_finseq_1(B,k1_numbers) ) => ( ( k2_relat_1(B) = k2_tarski(c1_6__jordan2c,A) & k3_finseq_1(B) = 2 & r1_xreal_0(c1_6__jordan2c,A) ) => ( k1_goboard1(B,1) = c1_6__jordan2c & k1_goboard1(B,2) = A ) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__jordan2c])],[i2_6_tmp__jordan2c,dh_c2_6__jordan2c]), [interesting(0.8),file(jordan2c,i1_6__jordan2c),[file(jordan2c,i1_6__jordan2c)]]). fof(i1_6_tmp__jordan2c,plain, ( m1_subset_1(c1_6__jordan2c,k1_numbers) => ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( ( v1_goboard1(B) & m2_finseq_1(B,k1_numbers) ) => ( ( k2_relat_1(B) = k2_tarski(c1_6__jordan2c,A) & k3_finseq_1(B) = 2 & r1_xreal_0(c1_6__jordan2c,A) ) => ( k1_goboard1(B,1) = c1_6__jordan2c & k1_goboard1(B,2) = A ) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__jordan2c])],[dt_c1_6__jordan2c,i1_6__jordan2c]), [interesting(1),t8_jordan2c]). fof(t8_jordan2c,theorem,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( ( v1_goboard1(C) & m2_finseq_1(C,k1_numbers) ) => ( ( k2_relat_1(C) = k2_tarski(A,B) & k3_finseq_1(C) = 2 & r1_xreal_0(A,B) ) => ( k1_goboard1(C,1) = A & k1_goboard1(C,2) = B ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_6_tmp__jordan2c,dh_c1_6__jordan2c]), [interesting(1),file(jordan2c,t8_jordan2c),[file(jordan2c,t8_jordan2c)]]).