% Mizar ND problem: t3_borsuk_5,borsuk_5,60,65 fof(dh_c1_2__borsuk_5,definition, ( ! [A,B,C,D,E] : k4_enumset1(c1_2__borsuk_5,A,B,C,D,E) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,B,E),k1_enumset1(A,C,D)) => ! [F,G,H,I,J,K] : k4_enumset1(F,G,H,I,J,K) = k2_xboole_0(k1_enumset1(F,H,K),k1_enumset1(G,I,J)) ), introduced(definition,[new_symbol(c1_2__borsuk_5),file(borsuk_5,c1_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c1_2__borsuk_5)]). fof(dh_c2_2__borsuk_5,definition, ( ! [A,B,C,D] : k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,A,B,C,D) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,A,D),k1_enumset1(c2_2__borsuk_5,B,C)) => ! [E,F,G,H,I] : k4_enumset1(c1_2__borsuk_5,E,F,G,H,I) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,F,I),k1_enumset1(E,G,H)) ), introduced(definition,[new_symbol(c2_2__borsuk_5),file(borsuk_5,c2_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c2_2__borsuk_5)]). fof(dh_c3_2__borsuk_5,definition, ( ! [A,B,C] : k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,A,B,C) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,C),k1_enumset1(c2_2__borsuk_5,A,B)) => ! [D,E,F,G] : k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,D,E,F,G) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,D,G),k1_enumset1(c2_2__borsuk_5,E,F)) ), introduced(definition,[new_symbol(c3_2__borsuk_5),file(borsuk_5,c3_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c3_2__borsuk_5)]). fof(dh_c4_2__borsuk_5,definition, ( ! [A,B] : k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,A,B) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,B),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,A)) => ! [C,D,E] : k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,C,D,E) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,E),k1_enumset1(c2_2__borsuk_5,C,D)) ), introduced(definition,[new_symbol(c4_2__borsuk_5),file(borsuk_5,c4_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c4_2__borsuk_5)]). fof(dh_c5_2__borsuk_5,definition, ( ! [A] : k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,A) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,A),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5)) => ! [B,C] : k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,B,C) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,C),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,B)) ), introduced(definition,[new_symbol(c5_2__borsuk_5),file(borsuk_5,c5_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c5_2__borsuk_5)]). fof(dh_c6_2__borsuk_5,definition, ( k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5)) => ! [A] : k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,A) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,A),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5)) ), introduced(definition,[new_symbol(c6_2__borsuk_5),file(borsuk_5,c6_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c6_2__borsuk_5)]). fof(fc9_finset_1,theorem,( ! [A,B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) ), file(finset_1,fc9_finset_1), [interesting(0.9),axiom,file(finset_1,fc9_finset_1)]). fof(commutativity_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(idempotence_k2_xboole_0,theorem,( ! [A,B] : k2_xboole_0(A,A) = A ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_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(dt_k1_enumset1,axiom,( $true ), file(enumset1,k1_enumset1), [interesting(0.9),axiom,file(enumset1,k1_enumset1)]). fof(dt_k2_xboole_0,axiom,( $true ), file(xboole_0,k2_xboole_0), [interesting(0.9),axiom,file(xboole_0,k2_xboole_0)]). fof(dt_k4_enumset1,axiom,( $true ), file(enumset1,k4_enumset1), [interesting(0.9),axiom,file(enumset1,k4_enumset1)]). fof(dt_c1_2__borsuk_5,assumption,( $true ), introduced(assumption,[file(borsuk_5,c1_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c1_2__borsuk_5)]). fof(dt_c2_2__borsuk_5,assumption,( $true ), introduced(assumption,[file(borsuk_5,c2_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c2_2__borsuk_5)]). fof(dt_c3_2__borsuk_5,assumption,( $true ), introduced(assumption,[file(borsuk_5,c3_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c3_2__borsuk_5)]). fof(dt_c4_2__borsuk_5,assumption,( $true ), introduced(assumption,[file(borsuk_5,c4_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c4_2__borsuk_5)]). fof(dt_c5_2__borsuk_5,assumption,( $true ), introduced(assumption,[file(borsuk_5,c5_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c5_2__borsuk_5)]). fof(dt_c6_2__borsuk_5,assumption,( $true ), introduced(assumption,[file(borsuk_5,c6_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c6_2__borsuk_5)]). fof(fc3_finset_1,theorem,( ! [A,B,C] : v1_finset_1(k1_enumset1(A,B,C)) ), file(finset_1,fc3_finset_1), [interesting(0.9),axiom,file(finset_1,fc3_finset_1)]). fof(fc6_finset_1,theorem,( ! [A,B,C,D,E,F] : v1_finset_1(k4_enumset1(A,B,C,D,E,F)) ), file(finset_1,fc6_finset_1), [interesting(0.9),axiom,file(finset_1,fc6_finset_1)]). fof(d10_xboole_0,definition,( ! [A,B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) ), file(xboole_0,d10_xboole_0), [interesting(0.9),axiom,file(xboole_0,d10_xboole_0)]). 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(dt_c1_2_1__borsuk_5,assumption,( $true ), introduced(assumption,[file(borsuk_5,c1_2_1__borsuk_5)]), [interesting(0.65),axiom,file(borsuk_5,c1_2_1__borsuk_5)]). fof(d3_tarski,definition,( ! [A,B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ), file(tarski,d3_tarski), [interesting(0.9),axiom,file(tarski,d3_tarski)]). fof(dh_c1_2_1__borsuk_5,definition, ( ~ ( r2_hidden(c1_2_1__borsuk_5,k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5)) & ~ r2_hidden(c1_2_1__borsuk_5,k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5))) ) => ! [A] : ~ ( r2_hidden(A,k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5)) & ~ r2_hidden(A,k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5))) ) ), introduced(definition,[new_symbol(c1_2_1__borsuk_5),file(borsuk_5,c1_2_1__borsuk_5)]), [interesting(0.65),axiom,file(borsuk_5,c1_2_1__borsuk_5)]). fof(e1_2_1__borsuk_5,assumption,( r2_hidden(c1_2_1__borsuk_5,k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5)) ), introduced(assumption,[file(borsuk_5,e1_2_1__borsuk_5)]), [interesting(0.65),axiom,file(borsuk_5,e1_2_1__borsuk_5)]). 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(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_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(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(cc1_rat_1,theorem,( ! [A] : ( v1_rat_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(rat_1,cc1_rat_1), [interesting(0.9),axiom,file(rat_1,cc1_rat_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_rat_1,theorem,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) & v1_rat_1(A) ) ) ), file(rat_1,cc2_rat_1), [interesting(0.9),axiom,file(rat_1,cc2_rat_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_int_1,theorem,( ! [A] : ( v4_ordinal2(A) => v1_int_1(A) ) ), file(int_1,cc3_int_1), [interesting(0.9),axiom,file(int_1,cc3_int_1)]). fof(cc4_int_1,theorem,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(A) & v1_xreal_0(A) ) ) ), file(int_1,cc4_int_1), [interesting(0.9),axiom,file(int_1,cc4_int_1)]). 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(fc17_membered,theorem,( ! [A,B,C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => v1_membered(k1_enumset1(A,B,C)) ) ), file(membered,fc17_membered), [interesting(0.9),axiom,file(membered,fc17_membered)]). fof(fc18_membered,theorem,( ! [A,B,C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => ( v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) ) ) ), file(membered,fc18_membered), [interesting(0.9),axiom,file(membered,fc18_membered)]). fof(fc19_membered,theorem,( ! [A,B,C] : ( ( v1_rat_1(A) & v1_rat_1(B) & v1_rat_1(C) ) => ( v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) ) ) ), file(membered,fc19_membered), [interesting(0.9),axiom,file(membered,fc19_membered)]). fof(fc20_membered,theorem,( ! [A,B,C] : ( ( v1_int_1(A) & v1_int_1(B) & v1_int_1(C) ) => ( v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) ) ) ), file(membered,fc20_membered), [interesting(0.9),axiom,file(membered,fc20_membered)]). fof(fc21_membered,theorem,( ! [A,B,C] : ( ( v4_ordinal2(A) & v4_ordinal2(B) & v4_ordinal2(C) ) => ( v1_membered(k1_enumset1(A,B,C)) & v2_membered(k1_enumset1(A,B,C)) & v3_membered(k1_enumset1(A,B,C)) & v4_membered(k1_enumset1(A,B,C)) & v5_membered(k1_enumset1(A,B,C)) ) ) ), file(membered,fc21_membered), [interesting(0.9),axiom,file(membered,fc21_membered)]). 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_int_1,theorem,( ? [A] : v1_int_1(A) ), file(int_1,rc2_int_1), [interesting(0.9),axiom,file(int_1,rc2_int_1)]). fof(rc2_rat_1,theorem,( ? [A] : v1_rat_1(A) ), file(rat_1,rc2_rat_1), [interesting(0.9),axiom,file(rat_1,rc2_rat_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(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(cc1_membered,theorem,( ! [A] : ( v5_membered(A) => v4_membered(A) ) ), file(membered,cc1_membered), [interesting(0.9),axiom,file(membered,cc1_membered)]). 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_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(fc22_membered,theorem,( ! [A,B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) ), file(membered,fc22_membered), [interesting(0.9),axiom,file(membered,fc22_membered)]). fof(fc23_membered,theorem,( ! [A,B] : ( ( v2_membered(A) & v2_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc23_membered), [interesting(0.9),axiom,file(membered,fc23_membered)]). fof(fc24_membered,theorem,( ! [A,B] : ( ( v3_membered(A) & v3_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc24_membered), [interesting(0.9),axiom,file(membered,fc24_membered)]). fof(fc25_membered,theorem,( ! [A,B] : ( ( v4_membered(A) & v4_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc25_membered), [interesting(0.9),axiom,file(membered,fc25_membered)]). fof(fc26_membered,theorem,( ! [A,B] : ( ( v5_membered(A) & v5_membered(B) ) => ( v1_membered(k2_xboole_0(A,B)) & v2_membered(k2_xboole_0(A,B)) & v3_membered(k2_xboole_0(A,B)) & v4_membered(k2_xboole_0(A,B)) & v5_membered(k2_xboole_0(A,B)) ) ) ), file(membered,fc26_membered), [interesting(0.9),axiom,file(membered,fc26_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(t1_boole,theorem,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A ), file(boole,t1_boole), [interesting(0.9),axiom,file(boole,t1_boole)]). 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(dt_m1_subset_1,axiom,( $true ), file(subset_1,m1_subset_1), [interesting(0.9),axiom,file(subset_1,m1_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(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(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(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(d4_enumset1,definition,( ! [A,B,C,D,E,F,G] : ( G = k4_enumset1(A,B,C,D,E,F) <=> ! [H] : ( r2_hidden(H,G) <=> ~ ( H != A & H != B & H != C & H != D & H != E & H != F ) ) ) ), file(enumset1,d4_enumset1), [interesting(0.9),axiom,file(enumset1,d4_enumset1)]). fof(e2_2_1__borsuk_5,plain,( ~ ( c1_2_1__borsuk_5 != c1_2__borsuk_5 & c1_2_1__borsuk_5 != c2_2__borsuk_5 & c1_2_1__borsuk_5 != c3_2__borsuk_5 & c1_2_1__borsuk_5 != c4_2__borsuk_5 & c1_2_1__borsuk_5 != c5_2__borsuk_5 & c1_2_1__borsuk_5 != c6_2__borsuk_5 ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c1_2_1__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,e1_2_1__borsuk_5])],[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_rat_1,cc1_xreal_0,cc2_rat_1,cc2_xreal_0,cc3_int_1,cc4_int_1,cc7_xreal_0,rc1_xreal_0,rc2_int_1,rc2_rat_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_enumset1,dt_c1_2__borsuk_5,dt_c1_2_1__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,fc6_finset_1,t1_subset,t7_boole,e1_2_1__borsuk_5,d4_enumset1]), [interesting(0.65),file(borsuk_5,e2_2_1__borsuk_5),[file(borsuk_5,e2_2_1__borsuk_5)]]). fof(d1_enumset1,definition,( ! [A,B,C,D] : ( D = k1_enumset1(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ~ ( E != A & E != B & E != C ) ) ) ), file(enumset1,d1_enumset1), [interesting(0.9),axiom,file(enumset1,d1_enumset1)]). fof(e3_2_1__borsuk_5,plain, ( r2_hidden(c1_2_1__borsuk_5,k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5)) | r2_hidden(c1_2_1__borsuk_5,k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c1_2_1__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,e1_2_1__borsuk_5])],[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_rat_1,cc1_xreal_0,cc2_rat_1,cc2_xreal_0,cc3_int_1,cc4_int_1,cc7_xreal_0,fc17_membered,fc18_membered,fc19_membered,fc20_membered,fc21_membered,rc1_xreal_0,rc2_int_1,rc2_rat_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_enumset1,dt_c1_2__borsuk_5,dt_c1_2_1__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,fc3_finset_1,t1_subset,t7_boole,e2_2_1__borsuk_5,d1_enumset1]), [interesting(0.65),file(borsuk_5,e3_2_1__borsuk_5),[file(borsuk_5,e3_2_1__borsuk_5)]]). fof(d2_xboole_0,definition,( ! [A,B,C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) ), file(xboole_0,d2_xboole_0), [interesting(0.9),axiom,file(xboole_0,d2_xboole_0)]). fof(e4_2_1__borsuk_5,plain,( r2_hidden(c1_2_1__borsuk_5,k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c1_2_1__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,e1_2_1__borsuk_5])],[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_rat_1,cc1_xreal_0,cc2_rat_1,cc2_xreal_0,cc3_int_1,cc4_int_1,cc7_xreal_0,fc17_membered,fc18_membered,fc19_membered,fc20_membered,fc21_membered,rc1_xreal_0,rc2_int_1,rc2_rat_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,t1_boole,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,fc9_finset_1,rc1_finset_1,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_enumset1,dt_k2_xboole_0,dt_c1_2__borsuk_5,dt_c1_2_1__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,fc3_finset_1,t1_subset,t7_boole,e3_2_1__borsuk_5,d2_xboole_0]), [interesting(0.65),file(borsuk_5,e4_2_1__borsuk_5),[file(borsuk_5,e4_2_1__borsuk_5)]]). fof(i3_2_1__borsuk_5,theorem,( $true ), introduced(tautology,[file(borsuk_5,i3_2_1__borsuk_5)]), [interesting(0.65),trivial,file(borsuk_5,i3_2_1__borsuk_5)]). fof(i2_2_1__borsuk_5,plain,( r2_hidden(c1_2_1__borsuk_5,k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5))) ), inference(conclusion,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c1_2_1__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,e1_2_1__borsuk_5])],[e4_2_1__borsuk_5,i3_2_1__borsuk_5]), [interesting(0.65),file(borsuk_5,i2_2_1__borsuk_5),[file(borsuk_5,i2_2_1__borsuk_5)]]). fof(i1_2_1__borsuk_5,plain,( ~ ( r2_hidden(c1_2_1__borsuk_5,k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5)) & ~ r2_hidden(c1_2_1__borsuk_5,k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c1_2_1__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5]),discharge_asm(discharge,[e1_2_1__borsuk_5])],[e1_2_1__borsuk_5,i2_2_1__borsuk_5]), [interesting(0.65),file(borsuk_5,i1_2_1__borsuk_5),[file(borsuk_5,i1_2_1__borsuk_5)]]). fof(i1_2_1_tmp__borsuk_5,plain,( ~ ( r2_hidden(c1_2_1__borsuk_5,k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5)) & ~ r2_hidden(c1_2_1__borsuk_5,k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5))) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5]),discharge_asm(discharge,[dt_c1_2_1__borsuk_5])],[dt_c1_2_1__borsuk_5,i1_2_1__borsuk_5]), [interesting(0.8),e1_2__borsuk_5]). fof(e1_2__borsuk_5,plain,( r1_tarski(k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5),k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5))) ), inference(let,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5])],[i1_2_1_tmp__borsuk_5,fc9_finset_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_enumset1,dt_k2_xboole_0,dt_k4_enumset1,dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,fc3_finset_1,fc6_finset_1,d3_tarski,dh_c1_2_1__borsuk_5]), [interesting(0.8),file(borsuk_5,e1_2__borsuk_5),[file(borsuk_5,e1_2__borsuk_5)]]). fof(dt_c7_2__borsuk_5,assumption,( $true ), introduced(assumption,[file(borsuk_5,c7_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c7_2__borsuk_5)]). fof(dh_c7_2__borsuk_5,definition, ( ~ ( r2_hidden(c7_2__borsuk_5,k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5))) & ~ r2_hidden(c7_2__borsuk_5,k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5)) ) => ! [A] : ~ ( r2_hidden(A,k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5))) & ~ r2_hidden(A,k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5)) ) ), introduced(definition,[new_symbol(c7_2__borsuk_5),file(borsuk_5,c7_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,c7_2__borsuk_5)]). fof(e2_2__borsuk_5,assumption,( r2_hidden(c7_2__borsuk_5,k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5))) ), introduced(assumption,[file(borsuk_5,e2_2__borsuk_5)]), [interesting(0.8),axiom,file(borsuk_5,e2_2__borsuk_5)]). fof(e3_2__borsuk_5,plain, ( r2_hidden(c7_2__borsuk_5,k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5)) | r2_hidden(c7_2__borsuk_5,k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,dt_c7_2__borsuk_5,e2_2__borsuk_5])],[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_rat_1,cc1_xreal_0,cc2_rat_1,cc2_xreal_0,cc3_int_1,cc4_int_1,cc7_xreal_0,fc17_membered,fc18_membered,fc19_membered,fc20_membered,fc21_membered,rc1_xreal_0,rc2_int_1,rc2_rat_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc22_membered,fc23_membered,fc24_membered,fc25_membered,fc26_membered,fc6_membered,rc1_membered,t1_boole,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,fc9_finset_1,rc1_finset_1,t2_subset,t6_boole,t8_boole,commutativity_k2_xboole_0,idempotence_k2_xboole_0,antisymmetry_r2_hidden,dt_k1_enumset1,dt_k2_xboole_0,dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,dt_c7_2__borsuk_5,fc3_finset_1,t1_subset,t7_boole,e2_2__borsuk_5,d2_xboole_0]), [interesting(0.8),file(borsuk_5,e3_2__borsuk_5),[file(borsuk_5,e3_2__borsuk_5)]]). fof(e4_2__borsuk_5,plain,( ~ ( c7_2__borsuk_5 != c1_2__borsuk_5 & c7_2__borsuk_5 != c3_2__borsuk_5 & c7_2__borsuk_5 != c6_2__borsuk_5 & c7_2__borsuk_5 != c2_2__borsuk_5 & c7_2__borsuk_5 != c4_2__borsuk_5 & c7_2__borsuk_5 != c5_2__borsuk_5 ) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,dt_c7_2__borsuk_5,e2_2__borsuk_5])],[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_rat_1,cc1_xreal_0,cc2_rat_1,cc2_xreal_0,cc3_int_1,cc4_int_1,cc7_xreal_0,fc17_membered,fc18_membered,fc19_membered,fc20_membered,fc21_membered,rc1_xreal_0,rc2_int_1,rc2_rat_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k1_enumset1,dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,dt_c7_2__borsuk_5,fc3_finset_1,t1_subset,t7_boole,e3_2__borsuk_5,d1_enumset1]), [interesting(0.8),file(borsuk_5,e4_2__borsuk_5),[file(borsuk_5,e4_2__borsuk_5)]]). fof(e5_2__borsuk_5,plain,( r2_hidden(c7_2__borsuk_5,k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,dt_c7_2__borsuk_5,e2_2__borsuk_5])],[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_rat_1,cc1_xreal_0,cc2_rat_1,cc2_xreal_0,cc3_int_1,cc4_int_1,cc7_xreal_0,rc1_xreal_0,rc2_int_1,rc2_rat_1,dt_k1_xboole_0,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc2_membered,cc3_membered,cc4_membered,fc6_membered,rc1_membered,existence_m1_subset_1,dt_m1_subset_1,cc15_membered,cc1_finset_1,rc1_finset_1,t2_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,dt_k4_enumset1,dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,dt_c7_2__borsuk_5,fc6_finset_1,t1_subset,t7_boole,e4_2__borsuk_5,d4_enumset1]), [interesting(0.8),file(borsuk_5,e5_2__borsuk_5),[file(borsuk_5,e5_2__borsuk_5)]]). fof(i5_2__borsuk_5,theorem,( $true ), introduced(tautology,[file(borsuk_5,i5_2__borsuk_5)]), [interesting(0.8),trivial,file(borsuk_5,i5_2__borsuk_5)]). fof(i4_2__borsuk_5,plain,( r2_hidden(c7_2__borsuk_5,k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5)) ), inference(conclusion,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,dt_c7_2__borsuk_5,e2_2__borsuk_5])],[e5_2__borsuk_5,i5_2__borsuk_5]), [interesting(0.8),file(borsuk_5,i4_2__borsuk_5),[file(borsuk_5,i4_2__borsuk_5)]]). fof(i3_2__borsuk_5,plain,( ~ ( r2_hidden(c7_2__borsuk_5,k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5))) & ~ r2_hidden(c7_2__borsuk_5,k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,dt_c7_2__borsuk_5]),discharge_asm(discharge,[e2_2__borsuk_5])],[e2_2__borsuk_5,i4_2__borsuk_5]), [interesting(0.8),file(borsuk_5,i3_2__borsuk_5),[file(borsuk_5,i3_2__borsuk_5)]]). fof(i3_2_tmp__borsuk_5,plain,( ~ ( r2_hidden(c7_2__borsuk_5,k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5))) & ~ r2_hidden(c7_2__borsuk_5,k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5]),discharge_asm(discharge,[dt_c7_2__borsuk_5])],[dt_c7_2__borsuk_5,i3_2__borsuk_5]), [interesting(0.8),i2_2__borsuk_5]). fof(i2_2__borsuk_5,plain,( r1_tarski(k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5)),k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5)) ), inference(let,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5])],[i3_2_tmp__borsuk_5,fc9_finset_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_enumset1,dt_k2_xboole_0,dt_k4_enumset1,dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,fc3_finset_1,fc6_finset_1,d3_tarski,dh_c7_2__borsuk_5]), [interesting(0.8),file(borsuk_5,i2_2__borsuk_5),[file(borsuk_5,i2_2__borsuk_5)]]). fof(i1_2__borsuk_5,plain,( k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5)) ), inference(conclusion,[status(thm),assumptions([dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5])],[fc9_finset_1,commutativity_k2_xboole_0,idempotence_k2_xboole_0,reflexivity_r1_tarski,dt_k1_enumset1,dt_k2_xboole_0,dt_k4_enumset1,dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,fc3_finset_1,fc6_finset_1,d10_xboole_0,e1_2__borsuk_5,i2_2__borsuk_5]), [interesting(0.8),file(borsuk_5,i1_2__borsuk_5),[file(borsuk_5,i1_2__borsuk_5)]]). fof(i1_2_tmp__borsuk_5,plain,( k4_enumset1(c1_2__borsuk_5,c2_2__borsuk_5,c3_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5,c6_2__borsuk_5) = k2_xboole_0(k1_enumset1(c1_2__borsuk_5,c3_2__borsuk_5,c6_2__borsuk_5),k1_enumset1(c2_2__borsuk_5,c4_2__borsuk_5,c5_2__borsuk_5)) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5])],[dt_c1_2__borsuk_5,dt_c2_2__borsuk_5,dt_c3_2__borsuk_5,dt_c4_2__borsuk_5,dt_c5_2__borsuk_5,dt_c6_2__borsuk_5,i1_2__borsuk_5]), [interesting(1),t3_borsuk_5]). fof(t3_borsuk_5,theorem,( ! [A,B,C,D,E,F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_enumset1(A,C,F),k1_enumset1(B,D,E)) ), inference(let,[status(thm),assumptions([])],[i1_2_tmp__borsuk_5,dh_c1_2__borsuk_5,dh_c2_2__borsuk_5,dh_c3_2__borsuk_5,dh_c4_2__borsuk_5,dh_c5_2__borsuk_5,dh_c6_2__borsuk_5]), [interesting(1),file(borsuk_5,t3_borsuk_5),[file(borsuk_5,t3_borsuk_5)]]).