%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP637+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:08:15 AM UTC 2025
% Result : Theorem 0.37s 0.55s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP637+1 : TPTP v9.0.0. Released v3.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 19 16:33:33 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.37/0.55 % SZS status Theorem
% 0.37/0.55 % SZS output start Proof
% 0.37/0.55 tff(r1_tarski_type, type, (
% 0.37/0.55 r1_tarski: ( $i * $i ) > $o)).
% 0.37/0.55 tff(u1_struct_0_type, type, (
% 0.37/0.55 u1_struct_0: $i > $i)).
% 0.37/0.55 tff(tptp_fun_G_6_type, type, (
% 0.37/0.55 tptp_fun_G_6: $i)).
% 0.37/0.55 tff(tptp_fun_F_5_type, type, (
% 0.37/0.55 tptp_fun_F_5: $i)).
% 0.37/0.55 tff(k9_relat_1_type, type, (
% 0.37/0.55 k9_relat_1: ( $i * $i ) > $i)).
% 0.37/0.55 tff(tptp_fun_E_4_type, type, (
% 0.37/0.55 tptp_fun_E_4: $i)).
% 0.37/0.55 tff(tptp_fun_C_2_type, type, (
% 0.37/0.55 tptp_fun_C_2: $i)).
% 0.37/0.55 tff(tptp_fun_D_3_type, type, (
% 0.37/0.55 tptp_fun_D_3: $i)).
% 0.37/0.55 tff(k2_funct_2_type, type, (
% 0.37/0.55 k2_funct_2: ( $i * $i * $i * $i ) > $i)).
% 0.37/0.55 tff(tptp_fun_B_1_type, type, (
% 0.37/0.55 tptp_fun_B_1: $i)).
% 0.37/0.55 tff(tptp_fun_A_0_type, type, (
% 0.37/0.55 tptp_fun_A_0: $i)).
% 0.37/0.55 tff(m1_relset_1_type, type, (
% 0.37/0.55 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.37/0.55 tff(m2_relset_1_type, type, (
% 0.37/0.55 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.37/0.55 tff(m1_group_2_type, type, (
% 0.37/0.55 m1_group_2: ( $i * $i ) > $o)).
% 0.37/0.55 tff(m1_group_6_type, type, (
% 0.37/0.55 m1_group_6: ( $i * $i * $i ) > $o)).
% 0.37/0.55 tff(v1_group_6_type, type, (
% 0.37/0.55 v1_group_6: ( $i * $i * $i ) > $o)).
% 0.37/0.55 tff(v1_funct_2_type, type, (
% 0.37/0.55 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.37/0.55 tff(v1_funct_1_type, type, (
% 0.37/0.55 v1_funct_1: $i > $o)).
% 0.37/0.55 tff(l1_group_1_type, type, (
% 0.37/0.55 l1_group_1: $i > $o)).
% 0.37/0.55 tff(v4_group_1_type, type, (
% 0.37/0.55 v4_group_1: $i > $o)).
% 0.37/0.55 tff(v3_group_1_type, type, (
% 0.37/0.55 v3_group_1: $i > $o)).
% 0.37/0.55 tff(v3_struct_0_type, type, (
% 0.37/0.55 v3_struct_0: $i > $o)).
% 0.37/0.55 tff(k1_realset1_type, type, (
% 0.37/0.55 k1_realset1: ( $i * $i ) > $i)).
% 0.37/0.55 tff(u1_group_1_type, type, (
% 0.37/0.55 u1_group_1: $i > $i)).
% 0.37/0.55 tff(v1_relat_1_type, type, (
% 0.37/0.55 v1_relat_1: $i > $o)).
% 0.37/0.55 tff(m1_subset_1_type, type, (
% 0.37/0.55 m1_subset_1: ( $i * $i ) > $o)).
% 0.37/0.55 tff(k1_zfmisc_1_type, type, (
% 0.37/0.55 k1_zfmisc_1: $i > $i)).
% 0.37/0.55 tff(k2_zfmisc_1_type, type, (
% 0.37/0.55 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.37/0.55 tff(1,plain,
% 0.37/0.55 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 0.37/0.55 inference(bind,[status(th)],[])).
% 0.37/0.55 tff(2,plain,
% 0.37/0.55 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.37/0.55 inference(quant_intro,[status(thm)],[1])).
% 0.37/0.55 tff(3,plain,
% 0.37/0.55 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(4,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.37/0.55 tff(5,plain,
% 0.37/0.55 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.37/0.55 tff(6,plain,(
% 0.37/0.55 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.37/0.55 inference(skolemize,[status(sab)],[5])).
% 0.37/0.55 tff(7,plain,
% 0.37/0.55 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.37/0.55 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.37/0.55 tff(8,plain,
% 0.37/0.55 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))),
% 0.37/0.55 inference(quant_inst,[status(thm)],[])).
% 0.37/0.55 tff(9,plain,
% 0.37/0.55 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.37/0.55 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.37/0.55 tff(10,plain,
% 0.37/0.55 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(11,plain,
% 0.37/0.55 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(12,plain,
% 0.37/0.55 (((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(13,plain,
% 0.37/0.55 ((m1_group_2(D!3, A!0) & (m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> (m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 0.37/0.55 inference(rewrite,[status(thm)],[])).
% 0.37/0.55 tff(14,plain,
% 0.37/0.55 ((m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> (m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(15,plain,
% 0.37/0.56 ((~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))) <=> (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(16,plain,
% 0.37/0.56 ((m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))) <=> (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[15])).
% 0.37/0.56 tff(17,plain,
% 0.37/0.56 ((m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> (m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[16])).
% 0.37/0.56 tff(18,plain,
% 0.37/0.56 ((m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))) <=> (m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[17, 14])).
% 0.37/0.56 tff(19,plain,
% 0.37/0.56 ((m1_group_2(D!3, A!0) & (m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))) <=> (m1_group_2(D!3, A!0) & (m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[18])).
% 0.37/0.56 tff(20,plain,
% 0.37/0.56 ((m1_group_2(D!3, A!0) & (m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))) <=> (m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[19, 13])).
% 0.37/0.56 tff(21,plain,
% 0.37/0.56 (((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (m1_group_2(D!3, A!0) & (m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))))) <=> ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[20])).
% 0.37/0.56 tff(22,plain,
% 0.37/0.56 (((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (m1_group_2(D!3, A!0) & (m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))))) <=> (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[21, 12])).
% 0.37/0.56 tff(23,plain,
% 0.37/0.56 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (m1_group_2(D!3, A!0) & (m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))))) <=> (((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & (v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[22])).
% 0.37/0.56 tff(24,plain,
% 0.37/0.56 ((((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (m1_group_2(D!3, A!0) & (m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))))) <=> ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[23, 11])).
% 0.37/0.56 tff(25,plain,
% 0.37/0.56 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (m1_group_2(D!3, A!0) & (m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))))))) <=> (((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & ((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))))),
% 0.37/0.56 inference(monotonicity,[status(thm)],[24])).
% 0.37/0.56 tff(26,plain,
% 0.37/0.56 ((((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0)) & (((~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1)) & ((v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) & (m1_group_2(D!3, A!0) & (m1_group_2(E!4, A!0) & (m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))))))) <=> ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))))),
% 0.37/0.56 inference(transitivity,[status(thm)],[25, 10])).
% 0.37/0.56 tff(27,plain,
% 0.37/0.56 ((~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B))))))))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(28,plain,
% 0.37/0.56 ((~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_group_2(D, A) => ![E: $i] : (m1_group_2(E, A) => ![F: $i] : (m1_group_2(F, B) => ![G: $i] : (m1_group_2(G, B) => ((((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E)))) & m1_group_6(D, A, E)) => m1_group_6(F, B, G)))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B))))))))))),
% 0.37/0.56 inference(rewrite,[status(thm)],[])).
% 0.37/0.56 tff(29,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v3_group_1(B)) & v4_group_1(B)) & l1_group_1(B)) => ![C: $i] : ((((v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B))) & v1_group_6(C, A, B)) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B))) => ![D: $i] : (m1_group_2(D, A) => ![E: $i] : (m1_group_2(E, A) => ![F: $i] : (m1_group_2(F, B) => ![G: $i] : (m1_group_2(G, B) => ((((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E)))) & m1_group_6(D, A, E)) => m1_group_6(F, B, G)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t10_latsubgr')).
% 0.37/0.56 tff(30,plain,
% 0.37/0.56 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.37/0.56 tff(31,plain,
% 0.37/0.56 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.37/0.56 tff(32,plain,
% 0.37/0.56 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.37/0.56 tff(33,plain,
% 0.37/0.56 (~![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & v4_group_1(B) & l1_group_1(B))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, u1_struct_0(A), u1_struct_0(B)) & v1_group_6(C, A, B) & m2_relset_1(C, u1_struct_0(A), u1_struct_0(B)))) | ![D: $i] : ((~m1_group_2(D, A)) | ![E: $i] : ((~m1_group_2(E, A)) | ![F: $i] : ((~m1_group_2(F, B)) | ![G: $i] : (m1_group_6(F, B, G) | (~((u1_struct_0(F) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(D))) & (u1_struct_0(G) = k2_funct_2(u1_struct_0(A), u1_struct_0(B), C, u1_struct_0(E))) & m1_group_6(D, A, E))) | (~m1_group_2(G, B)))))))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[32, 27])).
% 0.37/0.56 tff(34,plain,
% 0.37/0.56 ((~v3_struct_0(A!0)) & v3_group_1(A!0) & v4_group_1(A!0) & l1_group_1(A!0) & (~v3_struct_0(B!1)) & v3_group_1(B!1) & v4_group_1(B!1) & l1_group_1(B!1) & v1_funct_1(C!2) & v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & v1_group_6(C!2, A!0, B!1) & m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) & m1_group_2(D!3, A!0) & m1_group_2(E!4, A!0) & m1_group_2(F!5, B!1) & (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1))))),
% 0.37/0.56 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.37/0.56 tff(35,plain,
% 0.37/0.56 (m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.37/0.56 inference(and_elim,[status(thm)],[34])).
% 0.37/0.56 tff(36,plain,
% 0.37/0.56 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.37/0.56 inference(tautology,[status(thm)],[])).
% 0.37/0.56 tff(37,plain,
% 0.37/0.56 ((~(m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)) <=> m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) | m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.37/0.56 tff(38,plain,
% 0.37/0.56 (m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.37/0.56 inference(unit_resolution,[status(thm)],[37, 9])).
% 0.37/0.56 tff(39,plain,
% 0.37/0.56 (^[A: $i, B: $i, C: $i, D: $i] : refl(((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))) <=> ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(40,plain,
% 0.37/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[39])).
% 0.37/0.57 tff(41,plain,
% 0.37/0.57 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) <=> (~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))), ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) <=> ((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))))), (((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> (((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))), (((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(42,plain,
% 0.37/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[41])).
% 0.37/0.57 tff(43,plain,
% 0.37/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(44,plain,
% 0.37/0.57 (^[A: $i, B: $i, C: $i, D: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) <=> (v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))), ((((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(45,plain,
% 0.37/0.57 (![A: $i, B: $i, C: $i, D: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D))) <=> ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[44])).
% 0.37/0.57 tff(46,axiom,(![A: $i, B: $i, C: $i, D: $i] : (((v1_funct_1(C) & v1_funct_2(C, A, B)) & m1_relset_1(C, A, B)) => (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k2_funct_2')).
% 0.37/0.57 tff(47,plain,
% 0.37/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.37/0.57 tff(48,plain,
% 0.37/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.37/0.57 tff(49,plain,(
% 0.37/0.57 ![A: $i, B: $i, C: $i, D: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, A, B) & m1_relset_1(C, A, B))) | (k2_funct_2(A, B, C, D) = k9_relat_1(C, D)))),
% 0.37/0.57 inference(skolemize,[status(sab)],[48])).
% 0.37/0.57 tff(50,plain,
% 0.37/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.37/0.57 tff(51,plain,
% 0.37/0.57 (![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.37/0.57 tff(52,plain,
% 0.37/0.57 (v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))),
% 0.37/0.57 inference(and_elim,[status(thm)],[34])).
% 0.37/0.57 tff(53,plain,
% 0.37/0.57 (v1_funct_1(C!2)),
% 0.37/0.57 inference(and_elim,[status(thm)],[34])).
% 0.37/0.57 tff(54,plain,
% 0.37/0.57 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(55,plain,
% 0.37/0.57 (((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(56,plain,
% 0.37/0.57 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4)))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[55])).
% 0.37/0.57 tff(57,plain,
% 0.37/0.57 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[56, 54])).
% 0.37/0.57 tff(58,plain,
% 0.37/0.57 ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(59,plain,
% 0.37/0.57 ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4)))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.37/0.57 tff(60,plain,
% 0.37/0.57 ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4)))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[59, 53, 52, 51])).
% 0.37/0.57 tff(61,plain,
% 0.37/0.57 (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4)) = k9_relat_1(C!2, u1_struct_0(E!4))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[60, 38])).
% 0.37/0.57 tff(62,plain,
% 0.37/0.57 (~(m1_group_6(F!5, B!1, G!6) | (~((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4))) | (~m1_group_2(G!6, B!1)))),
% 0.37/0.57 inference(and_elim,[status(thm)],[34])).
% 0.37/0.57 tff(63,plain,
% 0.37/0.57 ((u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))) & (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))) & m1_group_6(D!3, A!0, E!4)),
% 0.37/0.57 inference(or_elim,[status(thm)],[62])).
% 0.37/0.57 tff(64,plain,
% 0.37/0.57 (u1_struct_0(G!6) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(E!4))),
% 0.37/0.57 inference(and_elim,[status(thm)],[63])).
% 0.37/0.57 tff(65,plain,
% 0.37/0.57 (u1_struct_0(G!6) = k9_relat_1(C!2, u1_struct_0(E!4))),
% 0.37/0.57 inference(transitivity,[status(thm)],[64, 61])).
% 0.37/0.57 tff(66,plain,
% 0.37/0.57 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(67,plain,
% 0.37/0.57 (((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1)))) <=> ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(68,plain,
% 0.37/0.57 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3)))))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[67])).
% 0.37/0.57 tff(69,plain,
% 0.37/0.57 (((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[68, 66])).
% 0.37/0.57 tff(70,plain,
% 0.37/0.57 ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | ((k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(71,plain,
% 0.37/0.57 ((~![A: $i, B: $i, C: $i, D: $i] : ((k2_funct_2(A, B, C, D) = k9_relat_1(C, D)) | (~v1_funct_1(C)) | (~v1_funct_2(C, A, B)) | (~m1_relset_1(C, A, B)))) | (~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (~v1_funct_1(C!2)) | (~v1_funct_2(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3)))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.37/0.57 tff(72,plain,
% 0.37/0.57 ((~m1_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3)))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[71, 53, 52, 51])).
% 0.37/0.57 tff(73,plain,
% 0.37/0.57 (k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3)) = k9_relat_1(C!2, u1_struct_0(D!3))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[72, 38])).
% 0.37/0.57 tff(74,plain,
% 0.37/0.57 (u1_struct_0(F!5) = k2_funct_2(u1_struct_0(A!0), u1_struct_0(B!1), C!2, u1_struct_0(D!3))),
% 0.37/0.57 inference(and_elim,[status(thm)],[63])).
% 0.37/0.57 tff(75,plain,
% 0.37/0.57 (u1_struct_0(F!5) = k9_relat_1(C!2, u1_struct_0(D!3))),
% 0.37/0.57 inference(transitivity,[status(thm)],[74, 73])).
% 0.37/0.57 tff(76,plain,
% 0.37/0.57 (r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6)) <=> r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4)))),
% 0.37/0.57 inference(monotonicity,[status(thm)],[75, 65])).
% 0.37/0.57 tff(77,plain,
% 0.37/0.57 (r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) <=> r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))),
% 0.37/0.57 inference(symmetry,[status(thm)],[76])).
% 0.37/0.57 tff(78,plain,
% 0.37/0.57 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(79,plain,
% 0.37/0.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[78])).
% 0.37/0.57 tff(80,plain,
% 0.37/0.57 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(81,plain,
% 0.37/0.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[80])).
% 0.37/0.57 tff(82,plain,
% 0.37/0.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[81, 79])).
% 0.37/0.57 tff(83,plain,
% 0.37/0.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(84,plain,
% 0.37/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[83])).
% 0.37/0.57 tff(85,plain,
% 0.37/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(86,plain,
% 0.37/0.57 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> (m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), rewrite((m1_group_2(B, A) => ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))), ((m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), (![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))) <=> ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(87,plain,
% 0.37/0.57 (![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[86])).
% 0.37/0.57 tff(88,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => (((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_group_2')).
% 0.37/0.57 tff(89,plain,
% 0.37/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.37/0.57 tff(90,plain,
% 0.37/0.57 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.37/0.57 tff(91,plain,(
% 0.37/0.57 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))))),
% 0.37/0.57 inference(skolemize,[status(sab)],[90])).
% 0.37/0.57 tff(92,plain,
% 0.37/0.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.37/0.57 tff(93,plain,
% 0.37/0.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[92, 82])).
% 0.37/0.57 tff(94,plain,
% 0.37/0.57 (l1_group_1(A!0)),
% 0.37/0.57 inference(and_elim,[status(thm)],[34])).
% 0.37/0.57 tff(95,plain,
% 0.37/0.57 (v3_group_1(A!0)),
% 0.37/0.57 inference(and_elim,[status(thm)],[34])).
% 0.37/0.57 tff(96,plain,
% 0.37/0.57 (~v3_struct_0(A!0)),
% 0.37/0.57 inference(and_elim,[status(thm)],[34])).
% 0.37/0.57 tff(97,plain,
% 0.37/0.57 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(98,plain,
% 0.37/0.57 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | (v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(99,plain,
% 0.37/0.57 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))) | v3_struct_0(A!0) | (~l1_group_1(A!0)) | (~v3_group_1(A!0)) | ![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.37/0.57 tff(100,plain,
% 0.37/0.57 (![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[99, 96, 95, 94, 93])).
% 0.37/0.57 tff(101,plain,
% 0.37/0.57 (m1_group_2(E!4, A!0)),
% 0.37/0.57 inference(and_elim,[status(thm)],[34])).
% 0.37/0.57 tff(102,plain,
% 0.37/0.57 (((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(E!4, A!0)) | (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(E!4, A!0)) | (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)))))),
% 0.37/0.57 inference(rewrite,[status(thm)],[])).
% 0.37/0.57 tff(103,plain,
% 0.37/0.57 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(E!4, A!0)) | (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)))))),
% 0.37/0.57 inference(quant_inst,[status(thm)],[])).
% 0.37/0.57 tff(104,plain,
% 0.37/0.57 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(E!4, A!0)) | (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4))))),
% 0.37/0.57 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.37/0.57 tff(105,plain,
% 0.37/0.57 (~(v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)))),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[104, 101, 100])).
% 0.37/0.57 tff(106,plain,
% 0.37/0.57 ((v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4))) | (~v3_struct_0(E!4))),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(107,plain,
% 0.37/0.57 (~v3_struct_0(E!4)),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.37/0.57 tff(108,plain,
% 0.37/0.57 ((v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4))) | v3_group_1(E!4)),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(109,plain,
% 0.37/0.57 (v3_group_1(E!4)),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[108, 105])).
% 0.37/0.57 tff(110,plain,
% 0.37/0.57 ((v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4))) | l1_group_1(E!4)),
% 0.37/0.57 inference(tautology,[status(thm)],[])).
% 0.37/0.57 tff(111,plain,
% 0.37/0.57 (l1_group_1(E!4)),
% 0.37/0.57 inference(unit_resolution,[status(thm)],[110, 105])).
% 0.37/0.57 tff(112,plain,
% 0.37/0.57 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(113,plain,
% 0.37/0.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[112])).
% 0.37/0.57 tff(114,plain,
% 0.37/0.57 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))))),
% 0.37/0.57 inference(bind,[status(th)],[])).
% 0.37/0.57 tff(115,plain,
% 0.37/0.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))),
% 0.37/0.57 inference(quant_intro,[status(thm)],[114])).
% 0.37/0.57 tff(116,plain,
% 0.37/0.57 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))),
% 0.37/0.57 inference(transitivity,[status(thm)],[115, 113])).
% 0.37/0.57 tff(117,plain,
% 0.37/0.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)) <=> (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))), ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> (~(~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))))), rewrite((~(~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))), ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))))), trans(trans(monotonicity(rewrite((r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))), ((m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> (m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))), rewrite((m1_group_2(B, A) <=> (~((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))), ((m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))), rewrite((~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))) <=> (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))), ((m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> ((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))), rewrite(((v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B))) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))), (((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))))), (![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A))) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(118,plain,
% 0.37/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[117])).
% 0.37/0.58 tff(119,plain,
% 0.37/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(120,plain,
% 0.37/0.58 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) <=> ((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))), (((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> (((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))), rewrite((((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))), (((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))), (![B: $i] : ((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))) <=> ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))), (((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(121,plain,
% 0.37/0.58 (![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[120])).
% 0.37/0.58 tff(122,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v3_group_1(A)) & l1_group_1(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v3_group_1(B)) & l1_group_1(B)) => (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d5_group_2')).
% 0.37/0.58 tff(123,plain,
% 0.37/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.37/0.58 tff(124,plain,
% 0.37/0.58 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.37/0.58 tff(125,plain,(
% 0.37/0.58 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~((~v3_struct_0(B)) & v3_group_1(B) & l1_group_1(B))) | (m1_group_2(B, A) <=> (r1_tarski(u1_struct_0(B), u1_struct_0(A)) & (u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B)))))))),
% 0.37/0.58 inference(skolemize,[status(sab)],[124])).
% 0.37/0.58 tff(126,plain,
% 0.37/0.58 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.37/0.58 tff(127,plain,
% 0.37/0.58 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.37/0.58 tff(128,plain,
% 0.37/0.58 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))) | (v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))) <=> m1_group_2(B, E!4)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))) | v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))) <=> m1_group_2(B, E!4)))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(129,plain,
% 0.37/0.58 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))) | (v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))) <=> m1_group_2(B, E!4)))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(130,plain,
% 0.37/0.58 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(A))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(A), u1_struct_0(B))))) <=> m1_group_2(B, A)))))) | v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))) <=> m1_group_2(B, E!4))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.37/0.58 tff(131,plain,
% 0.37/0.58 (v3_struct_0(E!4) | (~l1_group_1(E!4)) | (~v3_group_1(E!4)) | ![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))) <=> m1_group_2(B, E!4))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[130, 127])).
% 0.37/0.58 tff(132,plain,
% 0.37/0.58 (![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))) <=> m1_group_2(B, E!4))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[131, 111, 109, 107])).
% 0.37/0.58 tff(133,plain,
% 0.37/0.58 (m1_group_2(D!3, A!0)),
% 0.37/0.58 inference(and_elim,[status(thm)],[34])).
% 0.37/0.58 tff(134,plain,
% 0.37/0.58 (((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(D!3, A!0)) | (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)))))) <=> ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(D!3, A!0)) | (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(135,plain,
% 0.37/0.58 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | ((~m1_group_2(D!3, A!0)) | (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(136,plain,
% 0.37/0.58 ((~![B: $i] : ((~m1_group_2(B, A!0)) | (~(v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)))))) | (~m1_group_2(D!3, A!0)) | (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3))))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.37/0.58 tff(137,plain,
% 0.37/0.58 (~(v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[136, 133, 100])).
% 0.37/0.58 tff(138,plain,
% 0.37/0.58 ((v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3))) | v3_group_1(D!3)),
% 0.37/0.58 inference(tautology,[status(thm)],[])).
% 0.37/0.58 tff(139,plain,
% 0.37/0.58 (v3_group_1(D!3)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.37/0.58 tff(140,plain,
% 0.37/0.58 ((v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3))) | l1_group_1(D!3)),
% 0.37/0.58 inference(tautology,[status(thm)],[])).
% 0.37/0.58 tff(141,plain,
% 0.37/0.58 (l1_group_1(D!3)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[140, 137])).
% 0.37/0.58 tff(142,plain,
% 0.37/0.58 ((v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3))) | (~v3_struct_0(D!3))),
% 0.37/0.58 inference(tautology,[status(thm)],[])).
% 0.37/0.58 tff(143,plain,
% 0.37/0.58 (~v3_struct_0(D!3)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[142, 137])).
% 0.37/0.58 tff(144,plain,
% 0.37/0.58 (((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))) <=> m1_group_2(B, E!4))))) | (v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)) | (~(((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))) <=> m1_group_2(D!3, E!4))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))) <=> m1_group_2(B, E!4))))) | v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)) | (~(((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))) <=> m1_group_2(D!3, E!4))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(145,plain,
% 0.37/0.58 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))) <=> m1_group_2(B, E!4))))) | (v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)) | (~(((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))) <=> m1_group_2(D!3, E!4))))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(146,plain,
% 0.37/0.58 ((~![B: $i] : (v3_struct_0(B) | (~l1_group_1(B)) | (~v3_group_1(B)) | (~(((~r1_tarski(u1_struct_0(B), u1_struct_0(E!4))) | (~(u1_group_1(B) = k1_realset1(u1_group_1(E!4), u1_struct_0(B))))) <=> m1_group_2(B, E!4))))) | v3_struct_0(D!3) | (~l1_group_1(D!3)) | (~v3_group_1(D!3)) | (~(((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))) <=> m1_group_2(D!3, E!4)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.37/0.58 tff(147,plain,
% 0.37/0.58 (~(((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))) <=> m1_group_2(D!3, E!4))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[146, 143, 141, 139, 132])).
% 0.37/0.58 tff(148,plain,
% 0.37/0.58 (^[A: $i, B: $i] : rewrite((v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(149,plain,
% 0.37/0.58 (![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[148])).
% 0.37/0.58 tff(150,plain,
% 0.37/0.58 (^[A: $i, B: $i] : refl((v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(151,plain,
% 0.37/0.58 (![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[150])).
% 0.37/0.58 tff(152,plain,
% 0.37/0.58 (^[A: $i, B: $i] : rewrite((v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(153,plain,
% 0.37/0.58 (![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[152])).
% 0.37/0.58 tff(154,plain,
% 0.37/0.58 (![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 0.37/0.58 inference(transitivity,[status(thm)],[153, 151])).
% 0.37/0.58 tff(155,plain,
% 0.37/0.58 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) <=> (~(v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))) <=> (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) <=> (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> ((v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))))), rewrite(((v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(156,plain,
% 0.37/0.58 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[155])).
% 0.37/0.58 tff(157,plain,
% 0.37/0.58 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(158,plain,
% 0.37/0.58 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) => ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) => ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A)) => ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))), (((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) => ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(159,plain,
% 0.37/0.58 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) => ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[158])).
% 0.37/0.58 tff(160,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) & m1_group_2(B, A)) => ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m1_group_6')).
% 0.37/0.58 tff(161,plain,
% 0.37/0.58 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.37/0.58 tff(162,plain,
% 0.37/0.58 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.37/0.58 tff(163,plain,(
% 0.37/0.58 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A) & m1_group_2(B, A))) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 0.37/0.58 inference(skolemize,[status(sab)],[162])).
% 0.37/0.58 tff(164,plain,
% 0.37/0.58 (![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.37/0.58 tff(165,plain,
% 0.37/0.58 (![A: $i, B: $i] : (v3_struct_0(A) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[164, 154])).
% 0.37/0.58 tff(166,plain,
% 0.37/0.58 (![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[165, 149])).
% 0.37/0.58 tff(167,plain,
% 0.37/0.58 (v4_group_1(A!0)),
% 0.37/0.58 inference(and_elim,[status(thm)],[34])).
% 0.37/0.58 tff(168,plain,
% 0.37/0.58 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(169,plain,
% 0.37/0.58 ((v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4))) <=> (v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(170,plain,
% 0.37/0.58 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4))))),
% 0.37/0.58 inference(monotonicity,[status(thm)],[169])).
% 0.37/0.58 tff(171,plain,
% 0.37/0.58 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))),
% 0.37/0.58 inference(transitivity,[status(thm)],[170, 168])).
% 0.37/0.58 tff(172,plain,
% 0.37/0.58 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v3_group_1(A!0)) | (~v4_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4)))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(173,plain,
% 0.37/0.58 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | v3_struct_0(A!0) | (~m1_group_2(E!4, A!0)) | (~v4_group_1(A!0)) | (~v3_group_1(A!0)) | (~l1_group_1(A!0)) | ![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4))),
% 0.37/0.58 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.37/0.58 tff(174,plain,
% 0.37/0.58 (![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[173, 96, 95, 167, 94, 101, 166])).
% 0.37/0.58 tff(175,plain,
% 0.37/0.58 ((~![C: $i] : (m1_group_6(C, A!0, E!4) <=> m1_group_2(C, E!4))) | (m1_group_6(D!3, A!0, E!4) <=> m1_group_2(D!3, E!4))),
% 0.37/0.58 inference(quant_inst,[status(thm)],[])).
% 0.37/0.58 tff(176,plain,
% 0.37/0.58 (m1_group_6(D!3, A!0, E!4) <=> m1_group_2(D!3, E!4)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.37/0.58 tff(177,plain,
% 0.37/0.58 (m1_group_6(D!3, A!0, E!4)),
% 0.37/0.58 inference(and_elim,[status(thm)],[63])).
% 0.37/0.58 tff(178,plain,
% 0.37/0.58 ((~(m1_group_6(D!3, A!0, E!4) <=> m1_group_2(D!3, E!4))) | (~m1_group_6(D!3, A!0, E!4)) | m1_group_2(D!3, E!4)),
% 0.37/0.58 inference(tautology,[status(thm)],[])).
% 0.37/0.58 tff(179,plain,
% 0.37/0.58 ((~(m1_group_6(D!3, A!0, E!4) <=> m1_group_2(D!3, E!4))) | m1_group_2(D!3, E!4)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.37/0.58 tff(180,plain,
% 0.37/0.58 (m1_group_2(D!3, E!4)),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[179, 176])).
% 0.37/0.58 tff(181,plain,
% 0.37/0.58 ((((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))) <=> m1_group_2(D!3, E!4)) | (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3)))))) | (~m1_group_2(D!3, E!4))),
% 0.37/0.58 inference(tautology,[status(thm)],[])).
% 0.37/0.58 tff(182,plain,
% 0.37/0.58 ((((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))) <=> m1_group_2(D!3, E!4)) | (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.37/0.58 tff(183,plain,
% 0.37/0.58 (~((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3)))))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[182, 147])).
% 0.37/0.58 tff(184,plain,
% 0.37/0.58 (((~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~(u1_group_1(D!3) = k1_realset1(u1_group_1(E!4), u1_struct_0(D!3))))) | r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))),
% 0.37/0.58 inference(tautology,[status(thm)],[])).
% 0.37/0.58 tff(185,plain,
% 0.37/0.58 (r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))),
% 0.37/0.58 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.37/0.58 tff(186,plain,
% 0.37/0.58 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(187,plain,
% 0.37/0.58 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[186])).
% 0.37/0.58 tff(188,plain,
% 0.37/0.58 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.37/0.58 inference(rewrite,[status(thm)],[])).
% 0.37/0.58 tff(189,plain,
% 0.37/0.58 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.37/0.58 inference(bind,[status(th)],[])).
% 0.37/0.58 tff(190,plain,
% 0.37/0.58 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.37/0.58 inference(quant_intro,[status(thm)],[189])).
% 0.37/0.58 tff(191,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_relset_1')).
% 0.37/0.59 tff(192,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.37/0.59 tff(193,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.37/0.59 tff(194,plain,(
% 0.37/0.59 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.37/0.59 inference(skolemize,[status(sab)],[193])).
% 0.37/0.59 tff(195,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.37/0.59 tff(196,plain,
% 0.37/0.59 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(197,plain,
% 0.37/0.59 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | ((~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(198,plain,
% 0.37/0.59 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) | (~m2_relset_1(C!2, u1_struct_0(A!0), u1_struct_0(B!1))) | m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.37/0.59 tff(199,plain,
% 0.37/0.59 (m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[198, 35, 195])).
% 0.37/0.59 tff(200,plain,
% 0.37/0.59 (^[A: $i, B: $i, C: $i] : refl((v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(201,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[200])).
% 0.37/0.59 tff(202,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(203,plain,
% 0.37/0.59 (^[A: $i, B: $i, C: $i] : rewrite((m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(204,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C)) <=> ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[203])).
% 0.37/0.59 tff(205,axiom,(![A: $i, B: $i, C: $i] : (m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))) => v1_relat_1(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_relset_1')).
% 0.37/0.59 tff(206,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.37/0.59 tff(207,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.37/0.59 tff(208,plain,(
% 0.37/0.59 ![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.37/0.59 inference(skolemize,[status(sab)],[207])).
% 0.37/0.59 tff(209,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[208, 201])).
% 0.37/0.59 tff(210,plain,
% 0.37/0.59 (((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(211,plain,
% 0.37/0.59 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | (v1_relat_1(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1))))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(212,plain,
% 0.37/0.59 ((~![A: $i, B: $i, C: $i] : (v1_relat_1(C) | (~m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B)))))) | v1_relat_1(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(B!1)))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.37/0.59 tff(213,plain,
% 0.37/0.59 (v1_relat_1(C!2)),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[212, 209, 199])).
% 0.37/0.59 tff(214,plain,
% 0.37/0.59 (^[A: $i, B: $i, C: $i] : refl((r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))) <=> (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(215,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[214])).
% 0.37/0.59 tff(216,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(217,plain,
% 0.37/0.59 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B))) <=> ((~r1_tarski(A, B)) | r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))), ((v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> (v1_relat_1(C) => ((~r1_tarski(A, B)) | r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))))), rewrite((v1_relat_1(C) => ((~r1_tarski(A, B)) | r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))), ((v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(218,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)))) <=> ![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[217])).
% 0.37/0.59 tff(219,axiom,(![A: $i, B: $i, C: $i] : (v1_relat_1(C) => (r1_tarski(A, B) => r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t156_relat_1')).
% 0.37/0.59 tff(220,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.37/0.59 tff(221,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.37/0.59 tff(222,plain,(
% 0.37/0.59 ![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.37/0.59 inference(skolemize,[status(sab)],[221])).
% 0.37/0.59 tff(223,plain,
% 0.37/0.59 (![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[222, 215])).
% 0.37/0.59 tff(224,plain,
% 0.37/0.59 (((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | ((~v1_relat_1(C!2)) | r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (~v1_relat_1(C!2)) | r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(225,plain,
% 0.37/0.59 ((r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~v1_relat_1(C!2))) <=> ((~v1_relat_1(C!2)) | r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(226,plain,
% 0.37/0.59 (((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~v1_relat_1(C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | ((~v1_relat_1(C!2)) | r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4)))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[225])).
% 0.37/0.59 tff(227,plain,
% 0.37/0.59 (((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~v1_relat_1(C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (~v1_relat_1(C!2)) | r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))))),
% 0.37/0.59 inference(transitivity,[status(thm)],[226, 224])).
% 0.37/0.59 tff(228,plain,
% 0.37/0.59 ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4))) | (~v1_relat_1(C!2)))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(229,plain,
% 0.37/0.59 ((~![A: $i, B: $i, C: $i] : (r1_tarski(k9_relat_1(C, A), k9_relat_1(C, B)) | (~r1_tarski(A, B)) | (~v1_relat_1(C)))) | (~v1_relat_1(C!2)) | r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.37/0.59 tff(230,plain,
% 0.37/0.59 (r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4))) | (~r1_tarski(u1_struct_0(D!3), u1_struct_0(E!4)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[229, 223, 213])).
% 0.37/0.59 tff(231,plain,
% 0.37/0.59 (r1_tarski(k9_relat_1(C!2, u1_struct_0(D!3)), k9_relat_1(C!2, u1_struct_0(E!4)))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[230, 185])).
% 0.37/0.59 tff(232,plain,
% 0.37/0.59 (r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[231, 77])).
% 0.37/0.59 tff(233,plain,
% 0.37/0.59 (m1_group_2(G!6, B!1)),
% 0.37/0.59 inference(or_elim,[status(thm)],[62])).
% 0.37/0.59 tff(234,plain,
% 0.37/0.59 (l1_group_1(B!1)),
% 0.37/0.59 inference(and_elim,[status(thm)],[34])).
% 0.37/0.59 tff(235,plain,
% 0.37/0.59 (v4_group_1(B!1)),
% 0.37/0.59 inference(and_elim,[status(thm)],[34])).
% 0.37/0.59 tff(236,plain,
% 0.37/0.59 (v3_group_1(B!1)),
% 0.37/0.59 inference(and_elim,[status(thm)],[34])).
% 0.37/0.59 tff(237,plain,
% 0.37/0.59 (~v3_struct_0(B!1)),
% 0.37/0.59 inference(and_elim,[status(thm)],[34])).
% 0.37/0.59 tff(238,plain,
% 0.37/0.59 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(239,plain,
% 0.37/0.59 ((v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6))) <=> (v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(240,plain,
% 0.37/0.59 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6))))),
% 0.37/0.59 inference(monotonicity,[status(thm)],[239])).
% 0.37/0.59 tff(241,plain,
% 0.37/0.59 (((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))),
% 0.37/0.59 inference(transitivity,[status(thm)],[240, 238])).
% 0.37/0.59 tff(242,plain,
% 0.37/0.59 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | (v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6)))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(243,plain,
% 0.37/0.59 ((~![A: $i, B: $i] : (v3_struct_0(A) | (~m1_group_2(B, A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | (~l1_group_1(A)) | ![C: $i] : (m1_group_6(C, A, B) <=> m1_group_2(C, B)))) | v3_struct_0(B!1) | (~m1_group_2(G!6, B!1)) | (~v4_group_1(B!1)) | (~v3_group_1(B!1)) | (~l1_group_1(B!1)) | ![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.37/0.59 tff(244,plain,
% 0.37/0.59 (![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[243, 237, 236, 235, 234, 233, 166])).
% 0.37/0.59 tff(245,plain,
% 0.37/0.59 ((~![C: $i] : (m1_group_6(C, B!1, G!6) <=> m1_group_2(C, G!6))) | (m1_group_6(F!5, B!1, G!6) <=> m1_group_2(F!5, G!6))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(246,plain,
% 0.37/0.59 (m1_group_6(F!5, B!1, G!6) <=> m1_group_2(F!5, G!6)),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[245, 244])).
% 0.37/0.59 tff(247,plain,
% 0.37/0.59 (~m1_group_6(F!5, B!1, G!6)),
% 0.37/0.59 inference(or_elim,[status(thm)],[62])).
% 0.37/0.59 tff(248,plain,
% 0.37/0.59 ((~(m1_group_6(F!5, B!1, G!6) <=> m1_group_2(F!5, G!6))) | m1_group_6(F!5, B!1, G!6) | (~m1_group_2(F!5, G!6))),
% 0.37/0.59 inference(tautology,[status(thm)],[])).
% 0.37/0.59 tff(249,plain,
% 0.37/0.59 ((~(m1_group_6(F!5, B!1, G!6) <=> m1_group_2(F!5, G!6))) | (~m1_group_2(F!5, G!6))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.37/0.59 tff(250,plain,
% 0.37/0.59 (~m1_group_2(F!5, G!6)),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[249, 246])).
% 0.37/0.59 tff(251,plain,
% 0.37/0.59 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(252,plain,
% 0.37/0.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[251])).
% 0.37/0.59 tff(253,plain,
% 0.37/0.59 (^[A: $i] : refl((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(254,plain,
% 0.37/0.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[253])).
% 0.37/0.59 tff(255,plain,
% 0.37/0.59 (^[A: $i] : rewrite((v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(256,plain,
% 0.37/0.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[255])).
% 0.37/0.59 tff(257,plain,
% 0.37/0.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.37/0.59 inference(transitivity,[status(thm)],[256, 254])).
% 0.37/0.59 tff(258,plain,
% 0.37/0.59 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) <=> (~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)))), ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))) <=> ((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))))), rewrite(((v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))), (((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))) <=> (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(259,plain,
% 0.37/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[258])).
% 0.37/0.59 tff(260,plain,
% 0.37/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(261,plain,
% 0.37/0.59 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))), (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) <=> ((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C)) <=> ((~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | m1_group_2(B, C))), ((m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C))) <=> (m1_group_2(C, A) => ((~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | m1_group_2(B, C))))), rewrite((m1_group_2(C, A) => ((~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | m1_group_2(B, C))) <=> (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))), ((m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C))) <=> (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))), (![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C))) <=> ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))), ((m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C)))) <=> (m1_group_2(B, A) => ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))), rewrite((m1_group_2(B, A) => ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) <=> ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))), ((m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C)))) <=> ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))))), (![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C)))) <=> ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C))))) <=> (((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))))), rewrite((((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A)) => ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))), ((((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C))))) <=> ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))))),
% 0.37/0.59 inference(bind,[status(th)],[])).
% 0.37/0.59 tff(262,plain,
% 0.37/0.59 (![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 0.37/0.59 inference(quant_intro,[status(thm)],[261])).
% 0.37/0.59 tff(263,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v3_group_1(A)) & v4_group_1(A)) & l1_group_1(A)) => ![B: $i] : (m1_group_2(B, A) => ![C: $i] : (m1_group_2(C, A) => (r1_tarski(u1_struct_0(B), u1_struct_0(C)) => m1_group_2(B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t66_group_2')).
% 0.37/0.59 tff(264,plain,
% 0.37/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.37/0.59 tff(265,plain,
% 0.37/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[264, 260])).
% 0.37/0.59 tff(266,plain,(
% 0.37/0.59 ![A: $i] : ((~((~v3_struct_0(A)) & v3_group_1(A) & v4_group_1(A) & l1_group_1(A))) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 0.37/0.59 inference(skolemize,[status(sab)],[265])).
% 0.37/0.59 tff(267,plain,
% 0.37/0.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[266, 259])).
% 0.37/0.59 tff(268,plain,
% 0.37/0.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))) | (~v3_group_1(A)) | (~v4_group_1(A)))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[267, 257])).
% 0.37/0.59 tff(269,plain,
% 0.37/0.59 (![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[268, 252])).
% 0.37/0.59 tff(270,plain,
% 0.37/0.59 (((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.59 tff(271,plain,
% 0.37/0.59 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))) | (v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1)))))),
% 0.37/0.59 inference(quant_inst,[status(thm)],[])).
% 0.37/0.59 tff(272,plain,
% 0.37/0.59 ((~![A: $i] : (v3_struct_0(A) | (~l1_group_1(A)) | (~v3_group_1(A)) | (~v4_group_1(A)) | ![B: $i] : ((~m1_group_2(B, A)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, A)))))) | v3_struct_0(B!1) | (~l1_group_1(B!1)) | (~v3_group_1(B!1)) | (~v4_group_1(B!1)) | ![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))),
% 0.37/0.59 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.37/0.59 tff(273,plain,
% 0.37/0.59 (![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))),
% 0.37/0.59 inference(unit_resolution,[status(thm)],[272, 237, 236, 235, 234, 269])).
% 0.37/0.59 tff(274,plain,
% 0.37/0.59 (m1_group_2(F!5, B!1)),
% 0.37/0.59 inference(and_elim,[status(thm)],[34])).
% 0.37/0.59 tff(275,plain,
% 0.37/0.59 (((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | ((~m1_group_2(F!5, B!1)) | ![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C)))))) <=> ((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | (~m1_group_2(F!5, B!1)) | ![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C)))))),
% 0.37/0.59 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(276,plain,
% 0.37/0.60 (((~m1_group_2(F!5, B!1)) | ![C: $i] : (m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))) | (~m1_group_2(C, B!1)))) <=> ((~m1_group_2(F!5, B!1)) | ![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C)))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(277,plain,
% 0.37/0.60 (((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | ((~m1_group_2(F!5, B!1)) | ![C: $i] : (m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) <=> ((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | ((~m1_group_2(F!5, B!1)) | ![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))))),
% 0.37/0.60 inference(monotonicity,[status(thm)],[276])).
% 0.37/0.60 tff(278,plain,
% 0.37/0.60 (((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | ((~m1_group_2(F!5, B!1)) | ![C: $i] : (m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) <=> ((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | (~m1_group_2(F!5, B!1)) | ![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C)))))),
% 0.37/0.60 inference(transitivity,[status(thm)],[277, 275])).
% 0.37/0.60 tff(279,plain,
% 0.37/0.60 ((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | ((~m1_group_2(F!5, B!1)) | ![C: $i] : (m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))) | (~m1_group_2(C, B!1))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(280,plain,
% 0.37/0.60 ((~![B: $i] : ((~m1_group_2(B, B!1)) | ![C: $i] : (m1_group_2(B, C) | (~r1_tarski(u1_struct_0(B), u1_struct_0(C))) | (~m1_group_2(C, B!1))))) | (~m1_group_2(F!5, B!1)) | ![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.37/0.60 tff(281,plain,
% 0.37/0.60 (![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[280, 274, 273])).
% 0.37/0.60 tff(282,plain,
% 0.37/0.60 (((~![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))) | ((~m1_group_2(G!6, B!1)) | m1_group_2(F!5, G!6) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))))) <=> ((~![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))) | (~m1_group_2(G!6, B!1)) | m1_group_2(F!5, G!6) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))))),
% 0.37/0.60 inference(rewrite,[status(thm)],[])).
% 0.37/0.60 tff(283,plain,
% 0.37/0.60 ((~![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))) | ((~m1_group_2(G!6, B!1)) | m1_group_2(F!5, G!6) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))))),
% 0.37/0.60 inference(quant_inst,[status(thm)],[])).
% 0.37/0.60 tff(284,plain,
% 0.37/0.60 ((~![C: $i] : ((~m1_group_2(C, B!1)) | m1_group_2(F!5, C) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(C))))) | (~m1_group_2(G!6, B!1)) | m1_group_2(F!5, G!6) | (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6)))),
% 0.37/0.60 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.37/0.60 tff(285,plain,
% 0.37/0.60 (~r1_tarski(u1_struct_0(F!5), u1_struct_0(G!6))),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[284, 233, 281, 250])).
% 0.37/0.60 tff(286,plain,
% 0.37/0.60 ($false),
% 0.37/0.60 inference(unit_resolution,[status(thm)],[285, 232])).
% 0.37/0.60 % SZS output end Proof
% 0.37/0.60 % E exiting
%------------------------------------------------------------------------------