% Mizar ND problem: t6_algspec1,algspec1,162,23 fof(dh_c1_6__algspec1,definition, ( ( ~ v1_xboole_0(c1_6__algspec1) => ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,c1_6__algspec1,B) & m2_relset_1(D,c1_6__algspec1,B) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) ) => ( r1_partfun1(D,E) => r1_partfun1(k16_lang1(c1_6__algspec1,B,D),k16_lang1(A,C,E)) ) ) ) ) ) ) ) => ! [F] : ( ~ v1_xboole_0(F) => ! [G] : ( ~ v1_xboole_0(G) => ! [H] : ( ~ v1_xboole_0(H) => ! [I] : ( ~ v1_xboole_0(I) => ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,F,H) & m2_relset_1(J,F,H) ) => ! [K] : ( ( v1_funct_1(K) & v1_funct_2(K,G,I) & m2_relset_1(K,G,I) ) => ( r1_partfun1(J,K) => r1_partfun1(k16_lang1(F,H,J),k16_lang1(G,I,K)) ) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c1_6__algspec1),file(algspec1,c1_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c1_6__algspec1)]). fof(dh_c2_6__algspec1,definition, ( ( ~ v1_xboole_0(c2_6__algspec1) => ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,c1_6__algspec1,A) & m2_relset_1(C,c1_6__algspec1,A) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,c2_6__algspec1,B) & m2_relset_1(D,c2_6__algspec1,B) ) => ( r1_partfun1(C,D) => r1_partfun1(k16_lang1(c1_6__algspec1,A,C),k16_lang1(c2_6__algspec1,B,D)) ) ) ) ) ) ) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ~ v1_xboole_0(F) => ! [G] : ( ~ v1_xboole_0(G) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,c1_6__algspec1,F) & m2_relset_1(H,c1_6__algspec1,F) ) => ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,E,G) & m2_relset_1(I,E,G) ) => ( r1_partfun1(H,I) => r1_partfun1(k16_lang1(c1_6__algspec1,F,H),k16_lang1(E,G,I)) ) ) ) ) ) ) ), introduced(definition,[new_symbol(c2_6__algspec1),file(algspec1,c2_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c2_6__algspec1)]). fof(dh_c3_6__algspec1,definition, ( ( ~ v1_xboole_0(c3_6__algspec1) => ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,c1_6__algspec1,c3_6__algspec1) & m2_relset_1(B,c1_6__algspec1,c3_6__algspec1) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,c2_6__algspec1,A) & m2_relset_1(C,c2_6__algspec1,A) ) => ( r1_partfun1(B,C) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,B),k16_lang1(c2_6__algspec1,A,C)) ) ) ) ) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,c1_6__algspec1,D) & m2_relset_1(F,c1_6__algspec1,D) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,c2_6__algspec1,E) & m2_relset_1(G,c2_6__algspec1,E) ) => ( r1_partfun1(F,G) => r1_partfun1(k16_lang1(c1_6__algspec1,D,F),k16_lang1(c2_6__algspec1,E,G)) ) ) ) ) ) ), introduced(definition,[new_symbol(c3_6__algspec1),file(algspec1,c3_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c3_6__algspec1)]). fof(dh_c4_6__algspec1,definition, ( ( ~ v1_xboole_0(c4_6__algspec1) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,c1_6__algspec1,c3_6__algspec1) & m2_relset_1(A,c1_6__algspec1,c3_6__algspec1) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,c2_6__algspec1,c4_6__algspec1) & m2_relset_1(B,c2_6__algspec1,c4_6__algspec1) ) => ( r1_partfun1(A,B) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,A),k16_lang1(c2_6__algspec1,c4_6__algspec1,B)) ) ) ) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,c1_6__algspec1,c3_6__algspec1) & m2_relset_1(D,c1_6__algspec1,c3_6__algspec1) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,c2_6__algspec1,C) & m2_relset_1(E,c2_6__algspec1,C) ) => ( r1_partfun1(D,E) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,D),k16_lang1(c2_6__algspec1,C,E)) ) ) ) ) ), introduced(definition,[new_symbol(c4_6__algspec1),file(algspec1,c4_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c4_6__algspec1)]). fof(dh_c5_6__algspec1,definition, ( ( ( v1_funct_1(c5_6__algspec1) & v1_funct_2(c5_6__algspec1,c1_6__algspec1,c3_6__algspec1) & m2_relset_1(c5_6__algspec1,c1_6__algspec1,c3_6__algspec1) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,c2_6__algspec1,c4_6__algspec1) & m2_relset_1(A,c2_6__algspec1,c4_6__algspec1) ) => ( r1_partfun1(c5_6__algspec1,A) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,A)) ) ) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,c1_6__algspec1,c3_6__algspec1) & m2_relset_1(B,c1_6__algspec1,c3_6__algspec1) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,c2_6__algspec1,c4_6__algspec1) & m2_relset_1(C,c2_6__algspec1,c4_6__algspec1) ) => ( r1_partfun1(B,C) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,B),k16_lang1(c2_6__algspec1,c4_6__algspec1,C)) ) ) ) ), introduced(definition,[new_symbol(c5_6__algspec1),file(algspec1,c5_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c5_6__algspec1)]). fof(dh_c6_6__algspec1,definition, ( ( ( v1_funct_1(c6_6__algspec1) & v1_funct_2(c6_6__algspec1,c2_6__algspec1,c4_6__algspec1) & m2_relset_1(c6_6__algspec1,c2_6__algspec1,c4_6__algspec1) ) => ( r1_partfun1(c5_6__algspec1,c6_6__algspec1) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1)) ) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,c2_6__algspec1,c4_6__algspec1) & m2_relset_1(A,c2_6__algspec1,c4_6__algspec1) ) => ( r1_partfun1(c5_6__algspec1,A) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,A)) ) ) ), introduced(definition,[new_symbol(c6_6__algspec1),file(algspec1,c6_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c6_6__algspec1)]). fof(dt_k13_finseq_1,axiom,( $true ), file(finseq_1,k13_finseq_1), [interesting(0.9),axiom,file(finseq_1,k13_finseq_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_finseq_2,axiom,( $true ), file(finseq_2,m1_finseq_2), [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]). 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(rc1_circcomb,theorem,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ), file(circcomb,rc1_circcomb), [interesting(0.9),axiom,file(circcomb,rc1_circcomb)]). 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(redefinition_k3_finseq_2,definition,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) ), file(finseq_2,k3_finseq_2), [interesting(0.9),axiom,file(finseq_2,k3_finseq_2)]). 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_zfmisc_1,axiom,( $true ), file(zfmisc_1,k1_zfmisc_1), [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]). fof(dt_k3_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(k3_finseq_2(A)) & m1_finseq_2(k3_finseq_2(A),A) ) ), file(finseq_2,k3_finseq_2), [interesting(0.9),axiom,file(finseq_2,k3_finseq_2)]). fof(dt_m1_relset_1,axiom,( $true ), file(relset_1,m1_relset_1), [interesting(0.9),axiom,file(relset_1,m1_relset_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_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(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(cc1_relat_1,theorem,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) ), file(relat_1,cc1_relat_1), [interesting(0.9),axiom,file(relat_1,cc1_relat_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(fc5_relat_1,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k1_relat_1(A)) ) ), file(relat_1,fc5_relat_1), [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]). fof(fc7_relat_1,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_relat_1(A)) & v1_relat_1(k1_relat_1(A)) ) ) ), file(relat_1,fc7_relat_1), [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]). fof(rc1_relat_1,theorem,( ? [A] : ( v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc1_relat_1), [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]). fof(rc1_xboole_0,theorem,( ? [A] : v1_xboole_0(A) ), file(xboole_0,rc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]). 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_relat_1,theorem,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) ), file(relat_1,rc2_relat_1), [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]). fof(rc2_xboole_0,theorem,( ? [A] : ~ v1_xboole_0(A) ), file(xboole_0,rc2_xboole_0), [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]). fof(commutativity_k3_xboole_0,theorem,( ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(idempotence_k3_xboole_0,theorem,( ! [A,B] : k3_xboole_0(A,A) = A ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(symmetry_r1_partfun1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( r1_partfun1(A,B) => r1_partfun1(B,A) ) ) ), file(partfun1,r1_partfun1), [interesting(0.9),axiom,file(partfun1,r1_partfun1)]). fof(reflexivity_r1_partfun1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => r1_partfun1(A,A) ) ), file(partfun1,r1_partfun1), [interesting(0.9),axiom,file(partfun1,r1_partfun1)]). 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_k4_relset_1,definition,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k4_relset_1(A,B,C) = k1_relat_1(C) ) ), file(relset_1,k4_relset_1), [interesting(0.9),axiom,file(relset_1,k4_relset_1)]). fof(dt_k16_lang1,axiom,( ! [A,B,C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) ) => ( v1_funct_1(k16_lang1(A,B,C)) & v1_funct_2(k16_lang1(A,B,C),k3_finseq_2(A),k3_finseq_2(B)) & m2_relset_1(k16_lang1(A,B,C),k3_finseq_2(A),k3_finseq_2(B)) ) ) ), file(lang1,k16_lang1), [interesting(0.9),axiom,file(lang1,k16_lang1)]). 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_relat_1,axiom,( $true ), file(relat_1,k1_relat_1), [interesting(0.9),axiom,file(relat_1,k1_relat_1)]). fof(dt_k3_xboole_0,axiom,( $true ), file(xboole_0,k3_xboole_0), [interesting(0.9),axiom,file(xboole_0,k3_xboole_0)]). fof(dt_k4_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k4_relset_1(A,B,C),k1_zfmisc_1(A)) ) ), file(relset_1,k4_relset_1), [interesting(0.9),axiom,file(relset_1,k4_relset_1)]). fof(dt_c1_6__algspec1,assumption,( ~ v1_xboole_0(c1_6__algspec1) ), introduced(assumption,[file(algspec1,c1_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c1_6__algspec1)]). fof(dt_c2_6__algspec1,assumption,( ~ v1_xboole_0(c2_6__algspec1) ), introduced(assumption,[file(algspec1,c2_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c2_6__algspec1)]). fof(dt_c3_6__algspec1,assumption,( ~ v1_xboole_0(c3_6__algspec1) ), introduced(assumption,[file(algspec1,c3_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c3_6__algspec1)]). fof(dt_c4_6__algspec1,assumption,( ~ v1_xboole_0(c4_6__algspec1) ), introduced(assumption,[file(algspec1,c4_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c4_6__algspec1)]). fof(dt_c5_6__algspec1,assumption, ( v1_funct_1(c5_6__algspec1) & v1_funct_2(c5_6__algspec1,c1_6__algspec1,c3_6__algspec1) & m2_relset_1(c5_6__algspec1,c1_6__algspec1,c3_6__algspec1) ), introduced(assumption,[file(algspec1,c5_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c5_6__algspec1)]). fof(dt_c6_6__algspec1,assumption, ( v1_funct_1(c6_6__algspec1) & v1_funct_2(c6_6__algspec1,c2_6__algspec1,c4_6__algspec1) & m2_relset_1(c6_6__algspec1,c2_6__algspec1,c4_6__algspec1) ), introduced(assumption,[file(algspec1,c6_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c6_6__algspec1)]). fof(fc1_relat_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k3_xboole_0(A,B)) ) ), file(relat_1,fc1_relat_1), [interesting(0.9),axiom,file(relat_1,fc1_relat_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(e2_6__algspec1,assumption,( ! [A] : ( r2_hidden(A,k3_xboole_0(k4_relset_1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),k4_relset_1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1))) => k1_funct_1(c5_6__algspec1,A) = k1_funct_1(c6_6__algspec1,A) ) ), introduced(assumption,[file(algspec1,e2_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,e2_6__algspec1)]). fof(d6_partfun1,definition,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_partfun1(A,B) <=> ! [C] : ( r2_hidden(C,k3_xboole_0(k1_relat_1(A),k1_relat_1(B))) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ), file(partfun1,d6_partfun1), [interesting(0.9),axiom,file(partfun1,d6_partfun1)]). fof(dt_c7_6__algspec1,assumption,( $true ), introduced(assumption,[file(algspec1,c7_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c7_6__algspec1)]). fof(dh_c7_6__algspec1,definition, ( ~ ( r2_hidden(c7_6__algspec1,k3_xboole_0(k1_relat_1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1)),k1_relat_1(k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1)))) & k1_funct_1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),c7_6__algspec1) != k1_funct_1(k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1),c7_6__algspec1) ) => ! [A] : ~ ( r2_hidden(A,k3_xboole_0(k1_relat_1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1)),k1_relat_1(k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1)))) & k1_funct_1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),A) != k1_funct_1(k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1),A) ) ), introduced(definition,[new_symbol(c7_6__algspec1),file(algspec1,c7_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c7_6__algspec1)]). fof(e3_6__algspec1,assumption,( r2_hidden(c7_6__algspec1,k3_xboole_0(k4_relset_1(k3_finseq_2(c1_6__algspec1),k3_finseq_2(c3_6__algspec1),k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1)),k4_relset_1(k3_finseq_2(c2_6__algspec1),k3_finseq_2(c4_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1)))) ), introduced(assumption,[file(algspec1,e3_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,e3_6__algspec1)]). fof(rc1_pboole,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) ), file(pboole,rc1_pboole), [interesting(0.9),axiom,file(pboole,rc1_pboole)]). fof(rc2_catalg_1,theorem,( ? [A] : ( v1_relat_1(A) & ~ v3_relat_1(A) & v1_funct_1(A) ) ), file(catalg_1,rc2_catalg_1), [interesting(0.9),axiom,file(catalg_1,rc2_catalg_1)]). fof(rc3_relat_1,theorem,( ? [A] : ( v1_relat_1(A) & v3_relat_1(A) ) ), file(relat_1,rc3_relat_1), [interesting(0.9),axiom,file(relat_1,rc3_relat_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(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_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) ), file(finseq_2,m1_finseq_2), [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]). 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(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(dt_k1_xboole_0,axiom,( $true ), file(xboole_0,k1_xboole_0), [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]). 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(fc12_relat_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) & v3_relat_1(k1_xboole_0) ), file(relat_1,fc12_relat_1), [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]). fof(fc1_xboole_0,theorem,( v1_xboole_0(k1_xboole_0) ), file(xboole_0,fc1_xboole_0), [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]). fof(fc4_relat_1,theorem, ( v1_xboole_0(k1_xboole_0) & v1_relat_1(k1_xboole_0) ), file(relat_1,fc4_relat_1), [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]). 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_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(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_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ? [C] : m2_finseq_2(C,A,B) ) ), file(finseq_2,m2_finseq_2), [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]). 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_finseq_2,definition,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) ), file(finseq_2,m2_finseq_2), [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]). fof(dt_k1_numbers,axiom,( $true ), file(numbers,k1_numbers), [interesting(0.9),axiom,file(numbers,k1_numbers)]). fof(dt_k5_ordinal2,axiom,( $true ), file(ordinal2,k5_ordinal2), [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]). fof(dt_k5_relat_1,axiom,( ! [A,B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k5_relat_1(A,B)) ) ), file(relat_1,k5_relat_1), [interesting(0.9),axiom,file(relat_1,k5_relat_1)]). 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_m2_finseq_2,axiom,( ! [A,B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) ), file(finseq_2,m2_finseq_2), [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]). fof(fc10_relat_1,theorem,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(B,A)) & v1_relat_1(k5_relat_1(B,A)) ) ) ), file(relat_1,fc10_relat_1), [interesting(0.9),axiom,file(relat_1,fc10_relat_1)]). fof(fc1_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) ), file(funct_1,fc1_funct_1), [interesting(0.9),axiom,file(funct_1,fc1_funct_1)]). fof(fc9_relat_1,theorem,( ! [A,B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)) ) ) ), file(relat_1,fc9_relat_1), [interesting(0.9),axiom,file(relat_1,fc9_relat_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(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(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(redefinition_k15_lang1,definition,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_finseq_1(C,A) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) ) => k15_lang1(A,B,C,D) = k5_relat_1(C,D) ) ), file(lang1,k15_lang1), [interesting(0.9),axiom,file(lang1,k15_lang1)]). fof(redefinition_k5_numbers,definition,( k5_numbers = k5_ordinal2 ), file(numbers,k5_numbers), [interesting(0.9),axiom,file(numbers,k5_numbers)]). fof(dt_k15_lang1,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_finseq_1(C,A) & v1_funct_1(D) & v1_funct_2(D,A,B) & m1_relset_1(D,A,B) ) => m2_finseq_2(k15_lang1(A,B,C,D),B,k3_finseq_2(B)) ) ), file(lang1,k15_lang1), [interesting(0.9),axiom,file(lang1,k15_lang1)]). 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(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(de_c8_6__algspec1,definition,( c8_6__algspec1 = c7_6__algspec1 ), introduced(definition,[new_symbol(c8_6__algspec1),file(algspec1,c8_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c8_6__algspec1)]). fof(t2_boole,theorem,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ), file(boole,t2_boole), [interesting(0.9),axiom,file(boole,t2_boole)]). fof(d3_xboole_0,definition,( ! [A,B,C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) ), file(xboole_0,d3_xboole_0), [interesting(0.9),axiom,file(xboole_0,d3_xboole_0)]). fof(e4_6__algspec1,plain, ( r2_hidden(c7_6__algspec1,k4_relset_1(k3_finseq_2(c1_6__algspec1),k3_finseq_2(c3_6__algspec1),k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1))) & r2_hidden(c7_6__algspec1,k4_relset_1(k3_finseq_2(c2_6__algspec1),k3_finseq_2(c4_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1])],[rc1_circcomb,rc1_pboole,rc2_catalg_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,dt_k1_xboole_0,dt_k2_zfmisc_1,cc1_relset_1,cc2_funct_1,fc12_relat_1,fc1_relat_1,fc1_xboole_0,fc4_relat_1,fc5_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t2_boole,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_funct_1,cc1_relat_1,fc7_relat_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k3_finseq_2,redefinition_k4_relset_1,dt_k16_lang1,dt_k3_finseq_2,dt_k3_xboole_0,dt_k4_relset_1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,t1_subset,t7_boole,e3_6__algspec1,d3_xboole_0]), [interesting(0.8),file(algspec1,e4_6__algspec1),[file(algspec1,e4_6__algspec1)]]). fof(e5_6__algspec1,plain,( m2_finseq_2(c7_6__algspec1,c1_6__algspec1,k3_finseq_2(c1_6__algspec1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1])],[dt_k1_numbers,dt_k5_ordinal2,rc1_circcomb,rc1_pboole,rc2_catalg_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,existence_m1_finseq_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k5_numbers,dt_m1_finseq_1,cc1_relset_1,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,fc5_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,cc1_funct_1,cc1_relat_1,fc7_relat_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_finseq_2,redefinition_k3_finseq_2,redefinition_k4_relset_1,redefinition_m2_finseq_2,dt_k16_lang1,dt_k3_finseq_2,dt_k4_relset_1,dt_m2_finseq_2,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,t1_subset,t7_boole,e4_6__algspec1]), [interesting(0.8),file(algspec1,e5_6__algspec1),[file(algspec1,e5_6__algspec1)]]). fof(dt_c8_6__algspec1,plain,( m2_finseq_2(c8_6__algspec1,c1_6__algspec1,k3_finseq_2(c1_6__algspec1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,cc1_relset_1,rc1_circcomb,rc1_pboole,rc2_catalg_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_numbers,dt_m1_finseq_1,dt_m2_relset_1,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t1_subset,existence_m1_finseq_2,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_m1_finseq_2,dt_m1_subset_1,dt_m2_finseq_1,cc1_funct_1,cc1_relat_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m2_finseq_2,redefinition_k3_finseq_2,redefinition_m2_finseq_2,dt_k3_finseq_2,dt_m2_finseq_2,dt_c1_6__algspec1,dt_c7_6__algspec1,de_c8_6__algspec1,e5_6__algspec1]), [interesting(0.8),file(algspec1,c8_6__algspec1),[file(algspec1,c8_6__algspec1)]]). fof(de_c9_6__algspec1,definition,( c9_6__algspec1 = c7_6__algspec1 ), introduced(definition,[new_symbol(c9_6__algspec1),file(algspec1,c9_6__algspec1)]), [interesting(0.8),axiom,file(algspec1,c9_6__algspec1)]). fof(e6_6__algspec1,plain,( m2_finseq_2(c7_6__algspec1,c2_6__algspec1,k3_finseq_2(c2_6__algspec1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1])],[dt_k1_numbers,dt_k5_ordinal2,rc1_circcomb,rc1_pboole,rc2_catalg_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,existence_m1_finseq_1,redefinition_k5_numbers,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_k5_numbers,dt_m1_finseq_1,cc1_relset_1,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,fc5_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_relset_1,redefinition_m2_finseq_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_relset_1,cc1_funct_1,cc1_relat_1,fc7_relat_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_m2_finseq_2,redefinition_k3_finseq_2,redefinition_k4_relset_1,redefinition_m2_finseq_2,dt_k16_lang1,dt_k3_finseq_2,dt_k4_relset_1,dt_m2_finseq_2,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,t1_subset,t7_boole,e4_6__algspec1]), [interesting(0.8),file(algspec1,e6_6__algspec1),[file(algspec1,e6_6__algspec1)]]). fof(dt_c9_6__algspec1,plain,( m2_finseq_2(c9_6__algspec1,c2_6__algspec1,k3_finseq_2(c2_6__algspec1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1])],[reflexivity_r1_tarski,existence_m1_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_ordinal2,dt_m1_relset_1,cc1_relset_1,rc1_circcomb,rc1_pboole,rc2_catalg_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,t3_subset,t4_subset,t5_subset,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m2_relset_1,redefinition_k5_numbers,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k5_numbers,dt_m1_finseq_1,dt_m2_relset_1,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t1_subset,existence_m1_finseq_2,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_m1_finseq_2,dt_m1_subset_1,dt_m2_finseq_1,cc1_funct_1,cc1_relat_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_m2_finseq_2,redefinition_k3_finseq_2,redefinition_m2_finseq_2,dt_k3_finseq_2,dt_m2_finseq_2,dt_c2_6__algspec1,dt_c7_6__algspec1,de_c9_6__algspec1,e6_6__algspec1]), [interesting(0.8),file(algspec1,c9_6__algspec1),[file(algspec1,c9_6__algspec1)]]). fof(dh_c1_6_1__algspec1,definition, ( ( r2_hidden(c1_6_1__algspec1,k4_relset_1(k5_numbers,c1_6__algspec1,c8_6__algspec1)) => k1_funct_1(k15_lang1(c1_6__algspec1,c3_6__algspec1,c8_6__algspec1,c5_6__algspec1),c1_6_1__algspec1) = k1_funct_1(k15_lang1(c2_6__algspec1,c4_6__algspec1,c9_6__algspec1,c6_6__algspec1),c1_6_1__algspec1) ) => ! [A] : ( r2_hidden(A,k4_relset_1(k5_numbers,c1_6__algspec1,c8_6__algspec1)) => k1_funct_1(k15_lang1(c1_6__algspec1,c3_6__algspec1,c8_6__algspec1,c5_6__algspec1),A) = k1_funct_1(k15_lang1(c2_6__algspec1,c4_6__algspec1,c9_6__algspec1,c6_6__algspec1),A) ) ), introduced(definition,[new_symbol(c1_6_1__algspec1),file(algspec1,c1_6_1__algspec1)]), [interesting(0.65),axiom,file(algspec1,c1_6_1__algspec1)]). fof(e1_6_1__algspec1,assumption,( r2_hidden(c1_6_1__algspec1,k4_relset_1(k5_numbers,c1_6__algspec1,c8_6__algspec1)) ), introduced(assumption,[file(algspec1,e1_6_1__algspec1)]), [interesting(0.65),axiom,file(algspec1,e1_6_1__algspec1)]). fof(dt_c1_6_1__algspec1,assumption,( $true ), introduced(assumption,[file(algspec1,c1_6_1__algspec1)]), [interesting(0.65),axiom,file(algspec1,c1_6_1__algspec1)]). fof(dt_k2_relat_1,axiom,( $true ), file(relat_1,k2_relat_1), [interesting(0.9),axiom,file(relat_1,k2_relat_1)]). fof(fc6_relat_1,theorem,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k2_relat_1(A)) ) ), file(relat_1,fc6_relat_1), [interesting(0.9),axiom,file(relat_1,fc6_relat_1)]). fof(fc8_relat_1,theorem,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) ), file(relat_1,fc8_relat_1), [interesting(0.9),axiom,file(relat_1,fc8_relat_1)]). fof(redefinition_k5_relset_1,definition,( ! [A,B,C] : ( m1_relset_1(C,A,B) => k5_relset_1(A,B,C) = k2_relat_1(C) ) ), file(relset_1,k5_relset_1), [interesting(0.9),axiom,file(relset_1,k5_relset_1)]). fof(dt_k5_relset_1,axiom,( ! [A,B,C] : ( m1_relset_1(C,A,B) => m1_subset_1(k5_relset_1(A,B,C),k1_zfmisc_1(B)) ) ), file(relset_1,k5_relset_1), [interesting(0.9),axiom,file(relset_1,k5_relset_1)]). 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(e2_6_1__algspec1,plain, ( r2_hidden(k1_funct_1(c8_6__algspec1,c1_6_1__algspec1),k5_relset_1(k5_numbers,c1_6__algspec1,c8_6__algspec1)) & r2_hidden(k1_funct_1(c9_6__algspec1,c1_6_1__algspec1),k5_relset_1(k5_numbers,c2_6__algspec1,c9_6__algspec1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1,e1_6_1__algspec1])],[dt_k2_zfmisc_1,cc1_relset_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_finseq_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_2,redefinition_k3_finseq_2,redefinition_m2_finseq_2,dt_k1_numbers,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_2,dt_c7_6__algspec1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_relset_1,dt_k1_funct_1,dt_k1_relat_1,dt_k2_relat_1,dt_k4_relset_1,dt_k5_numbers,dt_k5_relset_1,dt_c1_6__algspec1,dt_c1_6_1__algspec1,dt_c2_6__algspec1,dt_c8_6__algspec1,dt_c9_6__algspec1,de_c8_6__algspec1,de_c9_6__algspec1,rc1_funct_1,t1_subset,t7_boole,e1_6_1__algspec1,d5_funct_1]), [interesting(0.65),file(algspec1,e2_6_1__algspec1),[file(algspec1,e2_6_1__algspec1)]]). fof(d1_funct_2,definition,( ! [A,B,C] : ( m2_relset_1(C,A,B) => ( ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ( v1_funct_2(C,A,B) <=> A = k4_relset_1(A,B,C) ) ) & ( B = k1_xboole_0 => ( A = k1_xboole_0 | ( v1_funct_2(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ), file(funct_2,d1_funct_2), [interesting(0.9),axiom,file(funct_2,d1_funct_2)]). fof(e1_6__algspec1,plain, ( k4_relset_1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1) = c1_6__algspec1 & k4_relset_1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1) = c2_6__algspec1 & k4_relset_1(k3_finseq_2(c1_6__algspec1),k3_finseq_2(c3_6__algspec1),k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1)) = k3_finseq_2(c1_6__algspec1) & k4_relset_1(k3_finseq_2(c2_6__algspec1),k3_finseq_2(c4_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1)) = k3_finseq_2(c2_6__algspec1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1])],[reflexivity_r1_tarski,antisymmetry_r2_hidden,rc1_circcomb,rc3_funct_1,t1_subset,t4_subset,t5_subset,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,dt_k13_finseq_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,cc1_funct_1,cc1_relat_1,cc1_relset_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_funct_1,rc1_pboole,rc1_relat_1,rc1_xboole_0,rc2_catalg_1,rc2_funct_1,rc2_relat_1,rc2_xboole_0,rc3_relat_1,rc4_funct_1,t2_subset,t3_subset,t7_boole,t8_boole,existence_m2_relset_1,redefinition_k3_finseq_2,redefinition_k4_relset_1,redefinition_m2_relset_1,dt_k16_lang1,dt_k1_xboole_0,dt_k3_finseq_2,dt_k4_relset_1,dt_m2_relset_1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,t6_boole,d1_funct_2]), [interesting(0.8),file(algspec1,e1_6__algspec1),[file(algspec1,e1_6__algspec1)]]). fof(e3_6_1__algspec1,plain,( r2_hidden(k1_funct_1(c8_6__algspec1,c1_6_1__algspec1),k3_xboole_0(k4_relset_1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),k4_relset_1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1))) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__algspec1,dt_c7_6__algspec1,e3_6__algspec1,e1_6_1__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1])],[existence_m1_finseq_1,dt_m1_finseq_1,rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m2_finseq_1,cc1_relset_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,t2_boole,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_relset_1,dt_c7_6__algspec1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_relat_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k3_finseq_2,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_relset_1,dt_k16_lang1,dt_k1_funct_1,dt_k3_finseq_2,dt_k3_xboole_0,dt_k4_relset_1,dt_k5_numbers,dt_k5_relset_1,dt_c1_6__algspec1,dt_c1_6_1__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c8_6__algspec1,dt_c9_6__algspec1,de_c8_6__algspec1,de_c9_6__algspec1,t1_subset,t7_boole,e2_6_1__algspec1,e1_6__algspec1,d3_xboole_0]), [interesting(0.65),file(algspec1,e3_6_1__algspec1),[file(algspec1,e3_6_1__algspec1)]]). fof(e1_6_1_1__algspec1,plain,( k1_funct_1(c5_6__algspec1,k1_funct_1(c8_6__algspec1,c1_6_1__algspec1)) = k1_funct_1(c6_6__algspec1,k1_funct_1(c9_6__algspec1,c1_6_1__algspec1)) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__algspec1,dt_c7_6__algspec1,e3_6__algspec1,e1_6_1__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,e2_6__algspec1])],[dt_k1_numbers,dt_k5_ordinal2,existence_m1_finseq_1,redefinition_k5_numbers,dt_k5_numbers,dt_m1_finseq_1,rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m2_finseq_1,cc1_relset_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,t2_boole,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_k3_finseq_2,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_relset_1,dt_c7_6__algspec1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_relat_1,fc5_relat_1,fc7_relat_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k4_relset_1,dt_k1_funct_1,dt_k3_xboole_0,dt_k4_relset_1,dt_c1_6__algspec1,dt_c1_6_1__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c8_6__algspec1,dt_c9_6__algspec1,de_c8_6__algspec1,de_c9_6__algspec1,t1_subset,t7_boole,e3_6_1__algspec1,e2_6__algspec1]), [interesting(0.5),file(algspec1,e1_6_1_1__algspec1),[file(algspec1,e1_6_1_1__algspec1)]]). fof(t23_funct_1,theorem,( ! [A,B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k1_relat_1(B)) => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ), file(funct_1,t23_funct_1), [interesting(0.9),axiom,file(funct_1,t23_funct_1)]). fof(e2_6_1_1__algspec1,plain,( k1_funct_1(c6_6__algspec1,k1_funct_1(c9_6__algspec1,c1_6_1__algspec1)) = k1_funct_1(k15_lang1(c2_6__algspec1,c4_6__algspec1,c9_6__algspec1,c6_6__algspec1),c1_6_1__algspec1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6_1__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1,e1_6_1__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m2_finseq_1,cc1_relset_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_k3_finseq_2,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_relset_1,dt_c7_6__algspec1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k15_lang1,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k15_lang1,dt_k1_funct_1,dt_k1_relat_1,dt_k4_relset_1,dt_k5_numbers,dt_k5_relat_1,dt_c1_6__algspec1,dt_c1_6_1__algspec1,dt_c2_6__algspec1,dt_c4_6__algspec1,dt_c6_6__algspec1,dt_c8_6__algspec1,dt_c9_6__algspec1,de_c8_6__algspec1,de_c9_6__algspec1,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e1_6_1__algspec1,t23_funct_1]), [interesting(0.5),file(algspec1,e2_6_1_1__algspec1),[file(algspec1,e2_6_1_1__algspec1)]]). fof(e4_6_1__algspec1,plain,( k1_funct_1(c5_6__algspec1,k1_funct_1(c8_6__algspec1,c1_6_1__algspec1)) = k1_funct_1(k15_lang1(c2_6__algspec1,c4_6__algspec1,c9_6__algspec1,c6_6__algspec1),c1_6_1__algspec1) ), inference(iterative_eq,[status(thm),assumptions([e2_6__algspec1,dt_c1_6_1__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1,e1_6_1__algspec1])],[e1_6_1_1__algspec1,e2_6_1_1__algspec1]), [interesting(0.65),file(algspec1,e4_6_1__algspec1),[file(algspec1,e4_6_1__algspec1)]]). fof(e5_6_1__algspec1,plain,( k1_funct_1(k15_lang1(c1_6__algspec1,c3_6__algspec1,c8_6__algspec1,c5_6__algspec1),c1_6_1__algspec1) = k1_funct_1(k15_lang1(c2_6__algspec1,c4_6__algspec1,c9_6__algspec1,c6_6__algspec1),c1_6_1__algspec1) ), inference(mizar_by,[status(thm),assumptions([e2_6__algspec1,dt_c1_6_1__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1,e1_6_1__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m2_finseq_1,cc1_relset_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_k3_finseq_2,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_relset_1,dt_c7_6__algspec1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k15_lang1,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k15_lang1,dt_k1_funct_1,dt_k1_relat_1,dt_k4_relset_1,dt_k5_numbers,dt_k5_relat_1,dt_c1_6__algspec1,dt_c1_6_1__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c8_6__algspec1,dt_c9_6__algspec1,de_c8_6__algspec1,de_c9_6__algspec1,fc1_funct_1,rc1_funct_1,t1_subset,t7_boole,e4_6_1__algspec1,e1_6_1__algspec1,t23_funct_1]), [interesting(0.65),file(algspec1,e5_6_1__algspec1),[file(algspec1,e5_6_1__algspec1)]]). fof(i3_6_1__algspec1,theorem,( $true ), introduced(tautology,[file(algspec1,i3_6_1__algspec1)]), [interesting(0.65),trivial,file(algspec1,i3_6_1__algspec1)]). fof(i2_6_1__algspec1,plain,( k1_funct_1(k15_lang1(c1_6__algspec1,c3_6__algspec1,c8_6__algspec1,c5_6__algspec1),c1_6_1__algspec1) = k1_funct_1(k15_lang1(c2_6__algspec1,c4_6__algspec1,c9_6__algspec1,c6_6__algspec1),c1_6_1__algspec1) ), inference(conclusion,[status(thm),assumptions([e2_6__algspec1,dt_c1_6_1__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1,e1_6_1__algspec1])],[e5_6_1__algspec1,i3_6_1__algspec1]), [interesting(0.65),file(algspec1,i2_6_1__algspec1),[file(algspec1,i2_6_1__algspec1)]]). fof(i1_6_1__algspec1,plain, ( r2_hidden(c1_6_1__algspec1,k4_relset_1(k5_numbers,c1_6__algspec1,c8_6__algspec1)) => k1_funct_1(k15_lang1(c1_6__algspec1,c3_6__algspec1,c8_6__algspec1,c5_6__algspec1),c1_6_1__algspec1) = k1_funct_1(k15_lang1(c2_6__algspec1,c4_6__algspec1,c9_6__algspec1,c6_6__algspec1),c1_6_1__algspec1) ), inference(discharge_asm,[status(thm),assumptions([e2_6__algspec1,dt_c1_6_1__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1]),discharge_asm(discharge,[e1_6_1__algspec1])],[e1_6_1__algspec1,i2_6_1__algspec1]), [interesting(0.65),file(algspec1,i1_6_1__algspec1),[file(algspec1,i1_6_1__algspec1)]]). fof(i1_6_1_tmp__algspec1,plain, ( r2_hidden(c1_6_1__algspec1,k4_relset_1(k5_numbers,c1_6__algspec1,c8_6__algspec1)) => k1_funct_1(k15_lang1(c1_6__algspec1,c3_6__algspec1,c8_6__algspec1,c5_6__algspec1),c1_6_1__algspec1) = k1_funct_1(k15_lang1(c2_6__algspec1,c4_6__algspec1,c9_6__algspec1,c6_6__algspec1),c1_6_1__algspec1) ), inference(discharge_asm,[status(thm),assumptions([e2_6__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1]),discharge_asm(discharge,[dt_c1_6_1__algspec1])],[dt_c1_6_1__algspec1,i1_6_1__algspec1]), [interesting(0.8),e10_6__algspec1]). fof(e10_6__algspec1,plain,( ! [A] : ( r2_hidden(A,k4_relset_1(k5_numbers,c1_6__algspec1,c8_6__algspec1)) => k1_funct_1(k15_lang1(c1_6__algspec1,c3_6__algspec1,c8_6__algspec1,c5_6__algspec1),A) = k1_funct_1(k15_lang1(c2_6__algspec1,c4_6__algspec1,c9_6__algspec1,c6_6__algspec1),A) ) ), inference(let,[status(thm),assumptions([e2_6__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1])],[i1_6_1_tmp__algspec1,dh_c1_6_1__algspec1]), [interesting(0.8),file(algspec1,e10_6__algspec1),[file(algspec1,e10_6__algspec1)]]). fof(redefinition_k8_funct_2,definition,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => k8_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ), file(funct_2,k8_funct_2), [interesting(0.9),axiom,file(funct_2,k8_funct_2)]). fof(dt_k8_funct_2,axiom,( ! [A,B,C,D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(C) & v1_funct_2(C,A,B) & m1_relset_1(C,A,B) & m1_subset_1(D,A) ) => m1_subset_1(k8_funct_2(A,B,C,D),B) ) ), file(funct_2,k8_funct_2), [interesting(0.9),axiom,file(funct_2,k8_funct_2)]). fof(d14_lang1,definition,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m2_relset_1(C,A,B) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k3_finseq_2(A),k3_finseq_2(B)) & m2_relset_1(D,k3_finseq_2(A),k3_finseq_2(B)) ) => ( D = k16_lang1(A,B,C) <=> ! [E] : ( m2_finseq_2(E,A,k3_finseq_2(A)) => k8_funct_2(k3_finseq_2(A),k3_finseq_2(B),D,E) = k15_lang1(A,B,E,C) ) ) ) ) ) ) ), file(lang1,d14_lang1), [interesting(0.9),axiom,file(lang1,d14_lang1)]). fof(e7_6__algspec1,plain, ( k1_funct_1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),c7_6__algspec1) = k15_lang1(c1_6__algspec1,c3_6__algspec1,c8_6__algspec1,c5_6__algspec1) & k1_funct_1(k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1),c7_6__algspec1) = k15_lang1(c2_6__algspec1,c4_6__algspec1,c9_6__algspec1,c6_6__algspec1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1])],[dt_k1_numbers,dt_k5_ordinal2,reflexivity_r1_tarski,redefinition_k5_numbers,dt_k5_numbers,rc1_circcomb,rc1_pboole,rc2_catalg_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k5_relat_1,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,cc1_relset_1,cc2_funct_1,fc10_relat_1,fc12_relat_1,fc1_funct_1,fc1_xboole_0,fc4_relat_1,fc9_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,existence_m2_finseq_2,existence_m2_relset_1,redefinition_k15_lang1,redefinition_k3_finseq_2,redefinition_k8_funct_2,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k15_lang1,dt_k16_lang1,dt_k1_funct_1,dt_k3_finseq_2,dt_k8_funct_2,dt_m2_finseq_2,dt_m2_relset_1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,dt_c8_6__algspec1,dt_c9_6__algspec1,de_c8_6__algspec1,de_c9_6__algspec1,cc1_funct_1,cc1_relat_1,rc1_xboole_0,rc2_xboole_0,t6_boole,t7_boole,t8_boole,d14_lang1]), [interesting(0.8),file(algspec1,e7_6__algspec1),[file(algspec1,e7_6__algspec1)]]). fof(e8_6__algspec1,plain, ( r1_tarski(k5_relset_1(k5_numbers,c1_6__algspec1,c8_6__algspec1),c1_6__algspec1) & r1_tarski(k5_relset_1(k5_numbers,c2_6__algspec1,c9_6__algspec1),c2_6__algspec1) ), inference(mizar_by,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1])],[dt_k2_zfmisc_1,cc1_relset_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,rc1_circcomb,rc1_pboole,rc2_catalg_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_m1_finseq_2,dt_m2_finseq_1,cc2_funct_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,fc6_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t1_subset,t4_subset,t5_subset,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_2,redefinition_k3_finseq_2,redefinition_m2_finseq_2,dt_k1_numbers,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k3_finseq_2,dt_k5_ordinal2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_2,dt_c7_6__algspec1,cc1_funct_1,cc1_relat_1,fc8_relat_1,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k5_numbers,redefinition_k5_relset_1,dt_k5_numbers,dt_k5_relset_1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c8_6__algspec1,dt_c9_6__algspec1,de_c8_6__algspec1,de_c9_6__algspec1,t3_subset]), [interesting(0.8),file(algspec1,e8_6__algspec1),[file(algspec1,e8_6__algspec1)]]). fof(t46_relat_1,theorem,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(k2_relat_1(A),k1_relat_1(B)) => k1_relat_1(k5_relat_1(A,B)) = k1_relat_1(A) ) ) ) ), file(relat_1,t46_relat_1), [interesting(0.9),axiom,file(relat_1,t46_relat_1)]). fof(e9_6__algspec1,plain, ( k4_relset_1(k5_numbers,c3_6__algspec1,k15_lang1(c1_6__algspec1,c3_6__algspec1,c8_6__algspec1,c5_6__algspec1)) = k4_relset_1(k5_numbers,c1_6__algspec1,c8_6__algspec1) & k4_relset_1(k5_numbers,c4_6__algspec1,k15_lang1(c2_6__algspec1,c4_6__algspec1,c9_6__algspec1,c6_6__algspec1)) = k4_relset_1(k5_numbers,c2_6__algspec1,c9_6__algspec1) ), inference(mizar_by,[status(thm),assumptions([dt_c7_6__algspec1,e3_6__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,antisymmetry_r2_hidden,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m2_finseq_1,cc1_relset_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,t1_subset,t4_subset,t5_subset,existence_m1_finseq_1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_relset_1,dt_c7_6__algspec1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc1_funct_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,fc9_relat_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,redefinition_k15_lang1,redefinition_k3_finseq_2,redefinition_k4_relset_1,redefinition_k5_numbers,redefinition_k5_relset_1,dt_k15_lang1,dt_k16_lang1,dt_k1_relat_1,dt_k2_relat_1,dt_k3_finseq_2,dt_k4_relset_1,dt_k5_numbers,dt_k5_relat_1,dt_k5_relset_1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c8_6__algspec1,dt_c9_6__algspec1,de_c8_6__algspec1,de_c9_6__algspec1,t3_subset,e8_6__algspec1,e1_6__algspec1,t46_relat_1]), [interesting(0.8),file(algspec1,e9_6__algspec1),[file(algspec1,e9_6__algspec1)]]). fof(t9_funct_1,theorem,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k1_relat_1(A) = k1_relat_1(B) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) => A = B ) ) ) ), file(funct_1,t9_funct_1), [interesting(0.9),axiom,file(funct_1,t9_funct_1)]). fof(e11_6__algspec1,plain,( k1_funct_1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),c7_6__algspec1) = k1_funct_1(k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1),c7_6__algspec1) ), inference(mizar_by,[status(thm),assumptions([e2_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1])],[rc1_pboole,rc2_catalg_1,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k13_finseq_1,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m2_finseq_1,cc1_relset_1,fc12_relat_1,fc1_xboole_0,fc4_relat_1,rc1_circcomb,rc3_funct_1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_k3_finseq_2,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_k5_ordinal2,dt_k5_relat_1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_relset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc10_relat_1,fc1_funct_1,fc5_relat_1,fc7_relat_1,fc9_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k15_lang1,redefinition_k4_relset_1,redefinition_k5_numbers,dt_k15_lang1,dt_k16_lang1,dt_k1_funct_1,dt_k1_relat_1,dt_k4_relset_1,dt_k5_numbers,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1,dt_c8_6__algspec1,dt_c9_6__algspec1,de_c8_6__algspec1,de_c9_6__algspec1,rc1_funct_1,t1_subset,t7_boole,e10_6__algspec1,e7_6__algspec1,e9_6__algspec1,t9_funct_1]), [interesting(0.8),file(algspec1,e11_6__algspec1),[file(algspec1,e11_6__algspec1)]]). fof(i7_6__algspec1,theorem,( $true ), introduced(tautology,[file(algspec1,i7_6__algspec1)]), [interesting(0.8),trivial,file(algspec1,i7_6__algspec1)]). fof(i6_6__algspec1,plain,( k1_funct_1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),c7_6__algspec1) = k1_funct_1(k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1),c7_6__algspec1) ), inference(conclusion,[status(thm),assumptions([e2_6__algspec1,dt_c7_6__algspec1,e3_6__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1])],[e11_6__algspec1,i7_6__algspec1]), [interesting(0.8),file(algspec1,i6_6__algspec1),[file(algspec1,i6_6__algspec1)]]). fof(i6_6_tmp__algspec1,plain, ( r2_hidden(c7_6__algspec1,k3_xboole_0(k4_relset_1(k3_finseq_2(c1_6__algspec1),k3_finseq_2(c3_6__algspec1),k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1)),k4_relset_1(k3_finseq_2(c2_6__algspec1),k3_finseq_2(c4_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1)))) => k1_funct_1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),c7_6__algspec1) = k1_funct_1(k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1),c7_6__algspec1) ), inference(discharge_asm,[status(thm),assumptions([e2_6__algspec1,dt_c7_6__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1]),discharge_asm(discharge,[e3_6__algspec1])],[e3_6__algspec1,i6_6__algspec1]), [interesting(0.8),i5_6__algspec1]). fof(i5_6__algspec1,plain,( ~ ( r2_hidden(c7_6__algspec1,k3_xboole_0(k1_relat_1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1)),k1_relat_1(k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1)))) & k1_funct_1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),c7_6__algspec1) != k1_funct_1(k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1),c7_6__algspec1) ) ), inference(mizar_def_expansion,[status(thm),assumptions([e2_6__algspec1,dt_c7_6__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1])],[i6_6_tmp__algspec1,dt_k2_zfmisc_1,cc1_relset_1,rc1_circcomb,rc3_funct_1,redefinition_m2_relset_1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc1_relat_1,fc5_relat_1,fc7_relat_1,rc1_funct_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,antisymmetry_r2_hidden,redefinition_k3_finseq_2,redefinition_k4_relset_1,dt_k16_lang1,dt_k1_funct_1,dt_k1_relat_1,dt_k3_finseq_2,dt_k3_xboole_0,dt_k4_relset_1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,dt_c7_6__algspec1]), [interesting(0.8),file(algspec1,i5_6__algspec1),[file(algspec1,i5_6__algspec1)]]). fof(i5_6_tmp__algspec1,plain,( ~ ( r2_hidden(c7_6__algspec1,k3_xboole_0(k1_relat_1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1)),k1_relat_1(k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1)))) & k1_funct_1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),c7_6__algspec1) != k1_funct_1(k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1),c7_6__algspec1) ) ), inference(discharge_asm,[status(thm),assumptions([e2_6__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1]),discharge_asm(discharge,[dt_c7_6__algspec1])],[dt_c7_6__algspec1,i5_6__algspec1]), [interesting(0.8),i4_6__algspec1]). fof(i4_6__algspec1,plain,( r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1)) ), inference(let,[status(thm),assumptions([e2_6__algspec1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1])],[i5_6_tmp__algspec1,dt_k13_finseq_1,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_m1_finseq_2,dt_m1_subset_1,cc1_relset_1,rc1_circcomb,rc3_funct_1,redefinition_k3_finseq_2,redefinition_m2_relset_1,dt_k3_finseq_2,dt_m1_relset_1,dt_m2_relset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,symmetry_r1_partfun1,reflexivity_r1_partfun1,antisymmetry_r2_hidden,dt_k16_lang1,dt_k1_funct_1,dt_k1_relat_1,dt_k3_xboole_0,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,fc1_relat_1,rc1_funct_1,d6_partfun1,dh_c7_6__algspec1]), [interesting(0.8),file(algspec1,i4_6__algspec1),[file(algspec1,i4_6__algspec1)]]). fof(i4_6_tmp__algspec1,plain, ( ! [A] : ( r2_hidden(A,k3_xboole_0(k4_relset_1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),k4_relset_1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1))) => k1_funct_1(c5_6__algspec1,A) = k1_funct_1(c6_6__algspec1,A) ) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1)) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1]),discharge_asm(discharge,[e2_6__algspec1])],[e2_6__algspec1,i4_6__algspec1]), [interesting(0.8),i3_6__algspec1]). fof(i3_6__algspec1,plain, ( r1_partfun1(c5_6__algspec1,c6_6__algspec1) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1)) ), inference(mizar_def_expansion,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1])],[i4_6_tmp__algspec1,d6_partfun1,dt_k13_finseq_1,dt_k2_zfmisc_1,dt_m1_finseq_2,cc1_relset_1,rc1_circcomb,rc3_funct_1,redefinition_k3_finseq_2,redefinition_m2_relset_1,dt_k1_zfmisc_1,dt_k3_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc5_relat_1,fc7_relat_1,rc1_relat_1,rc1_xboole_0,rc2_funct_1,rc2_relat_1,rc2_xboole_0,commutativity_k3_xboole_0,idempotence_k3_xboole_0,symmetry_r1_partfun1,reflexivity_r1_partfun1,antisymmetry_r2_hidden,redefinition_k4_relset_1,dt_k16_lang1,dt_k1_funct_1,dt_k1_relat_1,dt_k3_xboole_0,dt_k4_relset_1,dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1,dt_c6_6__algspec1,fc1_relat_1,rc1_funct_1]), [interesting(0.8),file(algspec1,i3_6__algspec1),[file(algspec1,i3_6__algspec1)]]). fof(i3_6_tmp__algspec1,plain, ( ( v1_funct_1(c6_6__algspec1) & v1_funct_2(c6_6__algspec1,c2_6__algspec1,c4_6__algspec1) & m2_relset_1(c6_6__algspec1,c2_6__algspec1,c4_6__algspec1) ) => ( r1_partfun1(c5_6__algspec1,c6_6__algspec1) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,c6_6__algspec1)) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1]),discharge_asm(discharge,[dt_c6_6__algspec1])],[dt_c6_6__algspec1,i3_6__algspec1]), [interesting(0.8),i2_6__algspec1]). fof(i2_6__algspec1,plain,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,c2_6__algspec1,c4_6__algspec1) & m2_relset_1(A,c2_6__algspec1,c4_6__algspec1) ) => ( r1_partfun1(c5_6__algspec1,A) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,A)) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,dt_c5_6__algspec1])],[i3_6_tmp__algspec1,dh_c6_6__algspec1]), [interesting(0.8),file(algspec1,i2_6__algspec1),[file(algspec1,i2_6__algspec1)]]). fof(i2_6_tmp__algspec1,plain, ( ( v1_funct_1(c5_6__algspec1) & v1_funct_2(c5_6__algspec1,c1_6__algspec1,c3_6__algspec1) & m2_relset_1(c5_6__algspec1,c1_6__algspec1,c3_6__algspec1) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,c2_6__algspec1,c4_6__algspec1) & m2_relset_1(A,c2_6__algspec1,c4_6__algspec1) ) => ( r1_partfun1(c5_6__algspec1,A) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,c5_6__algspec1),k16_lang1(c2_6__algspec1,c4_6__algspec1,A)) ) ) ), inference(discharge_asm,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1]),discharge_asm(discharge,[dt_c5_6__algspec1])],[dt_c5_6__algspec1,i2_6__algspec1]), [interesting(0.8),i1_6__algspec1]). fof(i1_6__algspec1,plain,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,c1_6__algspec1,c3_6__algspec1) & m2_relset_1(A,c1_6__algspec1,c3_6__algspec1) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,c2_6__algspec1,c4_6__algspec1) & m2_relset_1(B,c2_6__algspec1,c4_6__algspec1) ) => ( r1_partfun1(A,B) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,A),k16_lang1(c2_6__algspec1,c4_6__algspec1,B)) ) ) ) ), inference(let,[status(thm),assumptions([dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1])],[i2_6_tmp__algspec1,dh_c5_6__algspec1]), [interesting(0.8),file(algspec1,i1_6__algspec1),[file(algspec1,i1_6__algspec1)]]). fof(i1_6_tmp__algspec1,plain, ( ( ~ v1_xboole_0(c1_6__algspec1) & ~ v1_xboole_0(c2_6__algspec1) & ~ v1_xboole_0(c3_6__algspec1) & ~ v1_xboole_0(c4_6__algspec1) ) => ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,c1_6__algspec1,c3_6__algspec1) & m2_relset_1(A,c1_6__algspec1,c3_6__algspec1) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,c2_6__algspec1,c4_6__algspec1) & m2_relset_1(B,c2_6__algspec1,c4_6__algspec1) ) => ( r1_partfun1(A,B) => r1_partfun1(k16_lang1(c1_6__algspec1,c3_6__algspec1,A),k16_lang1(c2_6__algspec1,c4_6__algspec1,B)) ) ) ) ), inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1])],[dt_c1_6__algspec1,dt_c2_6__algspec1,dt_c3_6__algspec1,dt_c4_6__algspec1,i1_6__algspec1]), [interesting(1),t6_algspec1]). fof(t6_algspec1,theorem,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m2_relset_1(E,A,C) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,D) & m2_relset_1(F,B,D) ) => ( r1_partfun1(E,F) => r1_partfun1(k16_lang1(A,C,E),k16_lang1(B,D,F)) ) ) ) ) ) ) ) ), inference(let,[status(thm),assumptions([])],[i1_6_tmp__algspec1,dh_c1_6__algspec1,dh_c2_6__algspec1,dh_c3_6__algspec1,dh_c4_6__algspec1]), [interesting(1),file(algspec1,t6_algspec1),[file(algspec1,t6_algspec1)]]).