%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU451+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:28:01 AM UTC 2025
% Result : Theorem 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU451+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 07:28:24 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.39 % SZS status Theorem
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(k9_relset_2_type, type, (
% 0.21/0.39 k9_relset_2: ( $i * $i * $i * $i * $i ) > $i)).
% 0.21/0.39 tff(k6_partfun1_type, type, (
% 0.21/0.39 k6_partfun1: $i > $i)).
% 0.21/0.39 tff(tptp_fun_B_1_type, type, (
% 0.21/0.39 tptp_fun_B_1: $i)).
% 0.21/0.39 tff(tptp_fun_C_0_type, type, (
% 0.21/0.39 tptp_fun_C_0: $i)).
% 0.21/0.39 tff(tptp_fun_A_2_type, type, (
% 0.21/0.39 tptp_fun_A_2: $i)).
% 0.21/0.39 tff(k5_relat_1_type, type, (
% 0.21/0.39 k5_relat_1: ( $i * $i ) > $i)).
% 0.21/0.39 tff(k6_relat_1_type, type, (
% 0.21/0.39 k6_relat_1: $i > $i)).
% 0.21/0.39 tff(k7_relset_1_type, type, (
% 0.21/0.39 k7_relset_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.21/0.39 tff(m1_relset_1_type, type, (
% 0.21/0.39 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.21/0.39 tff(m2_relset_1_type, type, (
% 0.21/0.39 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.21/0.39 tff(v1_partfun1_type, type, (
% 0.21/0.39 v1_partfun1: ( $i * $i * $i ) > $o)).
% 0.21/0.39 tff(m1_subset_1_type, type, (
% 0.21/0.39 m1_subset_1: ( $i * $i ) > $o)).
% 0.21/0.39 tff(k1_zfmisc_1_type, type, (
% 0.21/0.39 k1_zfmisc_1: $i > $i)).
% 0.21/0.39 tff(k2_zfmisc_1_type, type, (
% 0.21/0.39 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.21/0.39 tff(1,plain,
% 0.21/0.39 ((k5_relat_1(C!0, k6_partfun1(B!1)) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1))) <=> (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1)))),
% 0.21/0.39 inference(commutativity,[status(thm)],[])).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (^[A: $i] : refl((k6_partfun1(A) = k6_relat_1(A)) <=> (k6_partfun1(A) = k6_relat_1(A)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A)) <=> ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A)) <=> ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(5,axiom,(![A: $i] : (k6_partfun1(A) = k6_relat_1(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k6_partfun1')).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.39 tff(7,plain,(
% 0.21/0.39 ![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.21/0.39 inference(skolemize,[status(sab)],[6])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (![A: $i] : (k6_partfun1(A) = k6_relat_1(A))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 ((~![A: $i] : (k6_partfun1(A) = k6_relat_1(A))) | (k6_partfun1(B!1) = k6_relat_1(B!1))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 (k6_partfun1(B!1) = k6_relat_1(B!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.21/0.39 tff(11,plain,
% 0.21/0.39 (k5_relat_1(C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))),
% 0.21/0.39 inference(monotonicity,[status(thm)],[10])).
% 0.21/0.39 tff(12,plain,
% 0.21/0.39 (k5_relat_1(C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))),
% 0.21/0.39 inference(symmetry,[status(thm)],[11])).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 (^[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)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 (![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))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.39 tff(15,plain,
% 0.21/0.39 (![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))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(16,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')).
% 0.21/0.39 tff(17,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.39 tff(18,plain,(
% 0.21/0.39 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.21/0.39 inference(skolemize,[status(sab)],[17])).
% 0.21/0.39 tff(19,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.39 tff(20,plain,
% 0.21/0.39 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_relat_1(B!1), B!1, B!1) <=> m1_relset_1(k6_relat_1(B!1), B!1, B!1))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(21,plain,
% 0.21/0.39 (m2_relset_1(k6_relat_1(B!1), B!1, B!1) <=> m1_relset_1(k6_relat_1(B!1), B!1, B!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.21/0.39 tff(22,plain,
% 0.21/0.39 (k6_relat_1(B!1) = k6_partfun1(B!1)),
% 0.21/0.39 inference(symmetry,[status(thm)],[10])).
% 0.21/0.39 tff(23,plain,
% 0.21/0.39 (m2_relset_1(k6_relat_1(B!1), B!1, B!1) <=> m2_relset_1(k6_partfun1(B!1), B!1, B!1)),
% 0.21/0.39 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.39 tff(24,plain,
% 0.21/0.39 (m2_relset_1(k6_partfun1(B!1), B!1, B!1) <=> m2_relset_1(k6_relat_1(B!1), B!1, B!1)),
% 0.21/0.39 inference(symmetry,[status(thm)],[23])).
% 0.21/0.39 tff(25,plain,
% 0.21/0.39 (^[A: $i] : refl((~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))) <=> (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(26,plain,
% 0.21/0.39 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))) <=> ![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.39 tff(27,plain,
% 0.21/0.39 (^[A: $i] : rewrite((v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A)) <=> (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(28,plain,
% 0.21/0.39 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A)) <=> ![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.39 tff(29,plain,
% 0.21/0.39 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A)) <=> ![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(30,axiom,(![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_partfun1')).
% 0.21/0.39 tff(31,plain,
% 0.21/0.39 (![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.21/0.39 tff(32,plain,(
% 0.21/0.39 ![A: $i] : (v1_partfun1(k6_partfun1(A), A, A) & m2_relset_1(k6_partfun1(A), A, A))),
% 0.21/0.39 inference(skolemize,[status(sab)],[31])).
% 0.21/0.39 tff(33,plain,
% 0.21/0.39 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.21/0.39 tff(34,plain,
% 0.21/0.39 (![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.21/0.39 tff(35,plain,
% 0.21/0.39 ((~![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))) | (~((~v1_partfun1(k6_partfun1(B!1), B!1, B!1)) | (~m2_relset_1(k6_partfun1(B!1), B!1, B!1))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(36,plain,
% 0.21/0.39 (~((~v1_partfun1(k6_partfun1(B!1), B!1, B!1)) | (~m2_relset_1(k6_partfun1(B!1), B!1, B!1)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.39 tff(37,plain,
% 0.21/0.39 (((~v1_partfun1(k6_partfun1(B!1), B!1, B!1)) | (~m2_relset_1(k6_partfun1(B!1), B!1, B!1))) | m2_relset_1(k6_partfun1(B!1), B!1, B!1)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 (m2_relset_1(k6_partfun1(B!1), B!1, B!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (m2_relset_1(k6_relat_1(B!1), B!1, B!1)),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 24])).
% 0.21/0.39 tff(40,plain,
% 0.21/0.39 ((~(m2_relset_1(k6_relat_1(B!1), B!1, B!1) <=> m1_relset_1(k6_relat_1(B!1), B!1, B!1))) | (~m2_relset_1(k6_relat_1(B!1), B!1, B!1)) | m1_relset_1(k6_relat_1(B!1), B!1, B!1)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (m1_relset_1(k6_relat_1(B!1), B!1, B!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[40, 39, 21])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(C!0, A!2, B!1) <=> m1_relset_1(C!0, A!2, B!1))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 (m2_relset_1(C!0, A!2, B!1) <=> m1_relset_1(C!0, A!2, B!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[42, 19])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))) <=> (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))) <=> (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(46,axiom,(~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t65_relset_2')).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[47, 44])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (k9_relset_2(A, A, B, k6_partfun1(A), C) = k9_relset_2(A, B, B, C, k6_partfun1(B))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[49, 44])).
% 0.21/0.39 tff(51,plain,(
% 0.21/0.39 ~((~m2_relset_1(C!0, A!2, B!1)) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[50])).
% 0.21/0.39 tff(52,plain,
% 0.21/0.39 (m2_relset_1(C!0, A!2, B!1)),
% 0.21/0.39 inference(or_elim,[status(thm)],[51])).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 ((~(m2_relset_1(C!0, A!2, B!1) <=> m1_relset_1(C!0, A!2, B!1))) | (~m2_relset_1(C!0, A!2, B!1)) | m1_relset_1(C!0, A!2, B!1)),
% 0.21/0.39 inference(tautology,[status(thm)],[])).
% 0.21/0.39 tff(54,plain,
% 0.21/0.39 ((~(m2_relset_1(C!0, A!2, B!1) <=> m1_relset_1(C!0, A!2, B!1))) | m1_relset_1(C!0, A!2, B!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.21/0.39 tff(55,plain,
% 0.21/0.39 (m1_relset_1(C!0, A!2, B!1)),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[54, 43])).
% 0.21/0.39 tff(56,plain,
% 0.21/0.39 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl(((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) <=> ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(57,plain,
% 0.21/0.39 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.39 tff(58,plain,
% 0.21/0.39 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) <=> (~((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))), ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) <=> (~(~((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))))), rewrite((~(~((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))) <=> ((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))), ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) <=> ((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))))), (((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> (((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))))), rewrite((((~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))), (((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : rewrite(((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) => (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) => (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.40 tff(63,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((m1_relset_1(E, A, B) & m1_relset_1(F, C, D)) => (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k7_relset_1')).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.21/0.40 tff(66,plain,(
% 0.21/0.40 ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~(m1_relset_1(E, A, B) & m1_relset_1(F, C, D))) | (k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[65])).
% 0.21/0.40 tff(67,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.21/0.40 tff(68,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.21/0.40 tff(69,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(70,plain,
% 0.21/0.40 (((k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1))) <=> ((~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(71,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1)))))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[70])).
% 0.21/0.40 tff(72,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))))),
% 0.21/0.40 inference(transitivity,[status(thm)],[71, 69])).
% 0.21/0.40 tff(73,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(74,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.40 tff(75,plain,
% 0.21/0.40 ((~m1_relset_1(k6_relat_1(B!1), B!1, B!1)) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[74, 68, 55])).
% 0.21/0.40 tff(76,plain,
% 0.21/0.40 (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k5_relat_1(C!0, k6_relat_1(B!1))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[75, 41])).
% 0.21/0.40 tff(77,plain,
% 0.21/0.40 (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1)) = k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1))),
% 0.21/0.40 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.40 tff(78,plain,
% 0.21/0.40 (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_relat_1(B!1))),
% 0.21/0.40 inference(symmetry,[status(thm)],[77])).
% 0.21/0.40 tff(79,plain,
% 0.21/0.40 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))) <=> ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(80,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[79])).
% 0.21/0.40 tff(81,plain,
% 0.21/0.40 (^[A: $i, B: $i, C: $i] : rewrite(((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(82,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.40 tff(83,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(84,plain,
% 0.21/0.40 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, A, B) => ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(85,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.40 tff(86,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) => ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_funct_2')).
% 0.21/0.40 tff(87,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.40 tff(88,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.21/0.40 tff(89,plain,(
% 0.21/0.40 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | ((k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C) & (k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))),
% 0.21/0.40 inference(skolemize,[status(sab)],[88])).
% 0.21/0.40 tff(90,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.21/0.40 tff(91,plain,
% 0.21/0.40 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.21/0.40 tff(92,plain,
% 0.21/0.40 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | ((~m2_relset_1(C!0, A!2, B!1)) | (~((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | (~m2_relset_1(C!0, A!2, B!1)) | (~((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(93,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | ((~m2_relset_1(C!0, A!2, B!1)) | (~((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0)))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(94,plain,
% 0.21/0.40 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | (~((~(k7_relset_1(A, A, A, B, k6_partfun1(A), C) = C)) | (~(k7_relset_1(A, B, B, B, C, k6_partfun1(B)) = C)))))) | (~m2_relset_1(C!0, A!2, B!1)) | (~((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.40 tff(95,plain,
% 0.21/0.40 (~((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[94, 52, 91])).
% 0.21/0.40 tff(96,plain,
% 0.21/0.40 (((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0))) | (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 (C!0 = k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1))),
% 0.21/0.41 inference(symmetry,[status(thm)],[97])).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 (((~(k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)) | (~(k7_relset_1(A!2, B!1, B!1, B!1, C!0, k6_partfun1(B!1)) = C!0))) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 (k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0) = C!0),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[99, 95])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 ((~![A: $i] : (k6_partfun1(A) = k6_relat_1(A))) | (k6_partfun1(A!2) = k6_relat_1(A!2))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 (k6_partfun1(A!2) = k6_relat_1(A!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[101, 8])).
% 0.21/0.41 tff(103,plain,
% 0.21/0.41 (k6_relat_1(A!2) = k6_partfun1(A!2)),
% 0.21/0.41 inference(symmetry,[status(thm)],[102])).
% 0.21/0.41 tff(104,plain,
% 0.21/0.41 (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k7_relset_1(A!2, A!2, A!2, B!1, k6_partfun1(A!2), C!0)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.41 tff(105,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(k6_relat_1(A!2), A!2, A!2) <=> m1_relset_1(k6_relat_1(A!2), A!2, A!2))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(106,plain,
% 0.21/0.41 (m2_relset_1(k6_relat_1(A!2), A!2, A!2) <=> m1_relset_1(k6_relat_1(A!2), A!2, A!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[105, 19])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 (m2_relset_1(k6_relat_1(A!2), A!2, A!2) <=> m2_relset_1(k6_partfun1(A!2), A!2, A!2)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 (m2_relset_1(k6_partfun1(A!2), A!2, A!2) <=> m2_relset_1(k6_relat_1(A!2), A!2, A!2)),
% 0.21/0.41 inference(symmetry,[status(thm)],[107])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 ((~![A: $i] : (~((~v1_partfun1(k6_partfun1(A), A, A)) | (~m2_relset_1(k6_partfun1(A), A, A))))) | (~((~v1_partfun1(k6_partfun1(A!2), A!2, A!2)) | (~m2_relset_1(k6_partfun1(A!2), A!2, A!2))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 (~((~v1_partfun1(k6_partfun1(A!2), A!2, A!2)) | (~m2_relset_1(k6_partfun1(A!2), A!2, A!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[109, 34])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 (((~v1_partfun1(k6_partfun1(A!2), A!2, A!2)) | (~m2_relset_1(k6_partfun1(A!2), A!2, A!2))) | m2_relset_1(k6_partfun1(A!2), A!2, A!2)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 (m2_relset_1(k6_partfun1(A!2), A!2, A!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.21/0.41 tff(113,plain,
% 0.21/0.41 (m2_relset_1(k6_relat_1(A!2), A!2, A!2)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.21/0.41 tff(114,plain,
% 0.21/0.41 ((~(m2_relset_1(k6_relat_1(A!2), A!2, A!2) <=> m1_relset_1(k6_relat_1(A!2), A!2, A!2))) | (~m2_relset_1(k6_relat_1(A!2), A!2, A!2)) | m1_relset_1(k6_relat_1(A!2), A!2, A!2)),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(115,plain,
% 0.21/0.41 (m1_relset_1(k6_relat_1(A!2), A!2, A!2)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[114, 113, 106])).
% 0.21/0.41 tff(116,plain,
% 0.21/0.41 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(117,plain,
% 0.21/0.41 (((k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (~m1_relset_1(C!0, A!2, B!1))) <=> ((~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(118,plain,
% 0.21/0.41 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (~m1_relset_1(C!0, A!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[117])).
% 0.21/0.41 tff(119,plain,
% 0.21/0.41 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (~m1_relset_1(C!0, A!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)))),
% 0.21/0.41 inference(transitivity,[status(thm)],[118, 116])).
% 0.21/0.41 tff(120,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | ((k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (~m1_relset_1(C!0, A!2, B!1)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(121,plain,
% 0.21/0.41 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((k7_relset_1(A, B, C, D, E, F) = k5_relat_1(E, F)) | (~m1_relset_1(E, A, B)) | (~m1_relset_1(F, C, D)))) | (~m1_relset_1(C!0, A!2, B!1)) | (~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.21/0.41 tff(122,plain,
% 0.21/0.41 ((~m1_relset_1(k6_relat_1(A!2), A!2, A!2)) | (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[121, 68, 55])).
% 0.21/0.41 tff(123,plain,
% 0.21/0.41 (k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[122, 115])).
% 0.21/0.41 tff(124,plain,
% 0.21/0.41 (k5_relat_1(k6_relat_1(A!2), C!0) = k7_relset_1(A!2, A!2, A!2, B!1, k6_relat_1(A!2), C!0)),
% 0.21/0.41 inference(symmetry,[status(thm)],[123])).
% 0.21/0.41 tff(125,plain,
% 0.21/0.41 (k5_relat_1(k6_partfun1(A!2), C!0) = k5_relat_1(k6_relat_1(A!2), C!0)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[102])).
% 0.21/0.41 tff(126,plain,
% 0.21/0.41 (^[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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(127,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.41 tff(128,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(129,plain,
% 0.21/0.41 (^[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)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(130,plain,
% 0.21/0.41 (![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))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.41 tff(131,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')).
% 0.21/0.41 tff(132,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.41 tff(133,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.21/0.41 tff(134,plain,(
% 0.21/0.41 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[133])).
% 0.21/0.41 tff(135,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, A, B)) | m1_subset_1(C, k1_zfmisc_1(k2_zfmisc_1(A, B))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.21/0.41 tff(136,plain,
% 0.21/0.41 (((~![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!0, A!2, B!1)) | m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, 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!0, A!2, B!1)) | m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(137,plain,
% 0.21/0.41 ((~![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!0, A!2, B!1)) | m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(138,plain,
% 0.21/0.41 ((~![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!0, A!2, B!1)) | m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.41 tff(139,plain,
% 0.21/0.41 (m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[138, 52, 135])).
% 0.21/0.41 tff(140,plain,
% 0.21/0.41 (m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2))) <=> m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[103])).
% 0.21/0.41 tff(141,plain,
% 0.21/0.41 (((~![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(k6_relat_1(A!2), A!2, A!2)) | m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2))))) <=> ((~![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(k6_relat_1(A!2), A!2, A!2)) | m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(142,plain,
% 0.21/0.41 ((~![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(k6_relat_1(A!2), A!2, A!2)) | m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(143,plain,
% 0.21/0.41 ((~![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(k6_relat_1(A!2), A!2, A!2)) | m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.21/0.41 tff(144,plain,
% 0.21/0.41 ((~m2_relset_1(k6_relat_1(A!2), A!2, A!2)) | m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[143, 135])).
% 0.21/0.41 tff(145,plain,
% 0.21/0.41 (m1_subset_1(k6_relat_1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[144, 113])).
% 0.21/0.41 tff(146,plain,
% 0.21/0.41 (m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[145, 140])).
% 0.21/0.41 tff(147,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : refl(((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) <=> ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(148,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[147])).
% 0.21/0.41 tff(149,plain,
% 0.21/0.41 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) <=> (~((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))))), ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) <=> (~(~((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))))))), rewrite((~(~((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))), ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) <=> ((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))))), (((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> (((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))))), rewrite((((~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))), (((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(150,plain,
% 0.21/0.41 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[149])).
% 0.21/0.42 tff(151,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(152,plain,
% 0.21/0.42 (^[A: $i, B: $i, C: $i, D: $i, E: $i] : rewrite(((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) => (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(153,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) => (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[152])).
% 0.21/0.42 tff(154,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i] : ((m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))) => (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k9_relset_2')).
% 0.21/0.42 tff(155,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.21/0.42 tff(156,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.21/0.42 tff(157,plain,(
% 0.21/0.42 ![A: $i, B: $i, C: $i, D: $i, E: $i] : ((~(m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B))) & m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C))))) | (k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[156])).
% 0.21/0.42 tff(158,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.21/0.42 tff(159,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[158, 148])).
% 0.21/0.42 tff(160,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(161,plain,
% 0.21/0.42 (((k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1))))) <=> ((~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(162,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[161])).
% 0.21/0.42 tff(163,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[162, 160])).
% 0.21/0.42 tff(164,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(165,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | (~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.21/0.42 tff(166,plain,
% 0.21/0.42 ((~m1_subset_1(k6_partfun1(A!2), k1_zfmisc_1(k2_zfmisc_1(A!2, A!2)))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[165, 159])).
% 0.21/0.42 tff(167,plain,
% 0.21/0.42 (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(k6_partfun1(A!2), C!0)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[166, 146, 139])).
% 0.21/0.42 tff(168,plain,
% 0.21/0.42 (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k5_relat_1(C!0, k6_partfun1(B!1))),
% 0.21/0.42 inference(transitivity,[status(thm)],[167, 125, 124, 104, 100, 98, 78, 76, 12])).
% 0.21/0.42 tff(169,plain,
% 0.21/0.42 ((k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1))) <=> (k5_relat_1(C!0, k6_partfun1(B!1)) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[168])).
% 0.21/0.42 tff(170,plain,
% 0.21/0.42 ((k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1))) <=> (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[169, 1])).
% 0.21/0.42 tff(171,plain,
% 0.21/0.42 ((k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))) <=> (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)))),
% 0.21/0.42 inference(symmetry,[status(thm)],[170])).
% 0.21/0.42 tff(172,plain,
% 0.21/0.42 (m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1))) <=> m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.42 tff(173,plain,
% 0.21/0.42 (((~![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(k6_relat_1(B!1), B!1, B!1)) | m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, 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(k6_relat_1(B!1), B!1, B!1)) | m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(174,plain,
% 0.21/0.42 ((~![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(k6_relat_1(B!1), B!1, B!1)) | m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(175,plain,
% 0.21/0.42 ((~![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(k6_relat_1(B!1), B!1, B!1)) | m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.21/0.42 tff(176,plain,
% 0.21/0.42 ((~m2_relset_1(k6_relat_1(B!1), B!1, B!1)) | m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[175, 135])).
% 0.21/0.42 tff(177,plain,
% 0.21/0.42 (m1_subset_1(k6_relat_1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[176, 39])).
% 0.21/0.42 tff(178,plain,
% 0.21/0.42 (m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[177, 172])).
% 0.21/0.42 tff(179,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(180,plain,
% 0.21/0.42 (((k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1))))) <=> ((~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(181,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1)))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[180])).
% 0.21/0.43 tff(182,plain,
% 0.21/0.43 (((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[181, 179])).
% 0.21/0.43 tff(183,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | ((k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(184,plain,
% 0.21/0.43 ((~![A: $i, B: $i, C: $i, D: $i, E: $i] : ((k9_relset_2(A, B, C, D, E) = k5_relat_1(D, E)) | (~m1_subset_1(D, k1_zfmisc_1(k2_zfmisc_1(A, B)))) | (~m1_subset_1(E, k1_zfmisc_1(k2_zfmisc_1(B, C)))))) | (~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.21/0.43 tff(185,plain,
% 0.21/0.43 ((~m1_subset_1(C!0, k1_zfmisc_1(k2_zfmisc_1(A!2, B!1)))) | (~m1_subset_1(k6_partfun1(B!1), k1_zfmisc_1(k2_zfmisc_1(B!1, B!1)))) | (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[184, 159])).
% 0.21/0.43 tff(186,plain,
% 0.21/0.43 (k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)) = k5_relat_1(C!0, k6_partfun1(B!1))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[185, 178, 139])).
% 0.21/0.43 tff(187,plain,
% 0.21/0.43 (k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[186, 171])).
% 0.21/0.43 tff(188,plain,
% 0.21/0.43 (~(k9_relset_2(A!2, A!2, B!1, k6_partfun1(A!2), C!0) = k9_relset_2(A!2, B!1, B!1, C!0, k6_partfun1(B!1)))),
% 0.21/0.43 inference(or_elim,[status(thm)],[51])).
% 0.21/0.43 tff(189,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[188, 187])).
% 0.21/0.43 % SZS output end Proof
% 0.21/0.43 % E exiting
%------------------------------------------------------------------------------