%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU444+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:27:59 AM UTC 2025
% Result : Theorem 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU444+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 07:24:03 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Theorem
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(k10_relset_1_type, type, (
% 0.20/0.38 k10_relset_1: ( $i * $i * $i * $i ) > $i)).
% 0.20/0.38 tff(k2_funct_5_type, type, (
% 0.20/0.38 k2_funct_5: $i > $i)).
% 0.20/0.38 tff(tptp_fun_C_0_type, type, (
% 0.20/0.38 tptp_fun_C_0: $i)).
% 0.20/0.38 tff(k6_relset_1_type, type, (
% 0.20/0.38 k6_relset_1: ( $i * $i * $i ) > $i)).
% 0.20/0.38 tff(tptp_fun_A_2_type, type, (
% 0.20/0.38 tptp_fun_A_2: $i)).
% 0.20/0.38 tff(tptp_fun_B_1_type, type, (
% 0.20/0.38 tptp_fun_B_1: $i)).
% 0.20/0.38 tff(k1_funct_5_type, type, (
% 0.20/0.38 k1_funct_5: $i > $i)).
% 0.20/0.38 tff(m2_relset_1_type, type, (
% 0.20/0.38 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.20/0.38 tff(1,plain,
% 0.20/0.38 (^[A: $i, B: $i, C: $i] : refl(((~m2_relset_1(C, B, A)) | (~((~(k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A))) | (~(k2_funct_5(C) = k10_relset_1(B, A, C, B)))))) <=> ((~m2_relset_1(C, B, A)) | (~((~(k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A))) | (~(k2_funct_5(C) = k10_relset_1(B, A, C, B)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | (~((~(k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A))) | (~(k2_funct_5(C) = k10_relset_1(B, A, C, B)))))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | (~((~(k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A))) | (~(k2_funct_5(C) = k10_relset_1(B, A, C, B))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (^[A: $i, B: $i, C: $i] : rewrite(((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k2_funct_5(C) = k10_relset_1(B, A, C, B)))) <=> ((~m2_relset_1(C, B, A)) | (~((~(k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A))) | (~(k2_funct_5(C) = k10_relset_1(B, A, C, B)))))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k2_funct_5(C) = k10_relset_1(B, A, C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | (~((~(k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A))) | (~(k2_funct_5(C) = k10_relset_1(B, A, C, B))))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.38 tff(5,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k2_funct_5(C) = k10_relset_1(B, A, C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k2_funct_5(C) = k10_relset_1(B, A, C, B))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (^[A: $i, B: $i, C: $i] : rewrite((m2_relset_1(C, B, A) => ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k2_funct_5(C) = k10_relset_1(B, A, C, B)))) <=> ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k2_funct_5(C) = k10_relset_1(B, A, C, B)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(7,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, B, A) => ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k2_funct_5(C) = k10_relset_1(B, A, C, B)))) <=> ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k2_funct_5(C) = k10_relset_1(B, A, C, B))))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.38 tff(8,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, B, A) => ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k2_funct_5(C) = k10_relset_1(B, A, C, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t51_relset_2')).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k2_funct_5(C) = k10_relset_1(B, A, C, B))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k2_funct_5(C) = k10_relset_1(B, A, C, B))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.38 tff(11,plain,(
% 0.20/0.38 ![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k2_funct_5(C) = k10_relset_1(B, A, C, B))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[10])).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | (~((~(k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A))) | (~(k2_funct_5(C) = k10_relset_1(B, A, C, B))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | (~((~(k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A))) | (~(k2_funct_5(C) = k10_relset_1(B, A, C, B))))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k10_relset_1(A, B, k6_relset_1(B, A, C), k10_relset_1(B, A, C, B)) = k10_relset_1(A, B, k6_relset_1(B, A, C), k2_funct_5(C)))))) <=> (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k10_relset_1(A, B, k6_relset_1(B, A, C), k10_relset_1(B, A, C, B)) = k10_relset_1(A, B, k6_relset_1(B, A, C), k2_funct_5(C))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, B, A) => ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k10_relset_1(A, B, k6_relset_1(B, A, C), k10_relset_1(B, A, C, B)) = k10_relset_1(A, B, k6_relset_1(B, A, C), k2_funct_5(C)))))) <=> (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k10_relset_1(A, B, k6_relset_1(B, A, C), k10_relset_1(B, A, C, B)) = k10_relset_1(A, B, k6_relset_1(B, A, C), k2_funct_5(C))))))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(16,axiom,(~![A: $i, B: $i, C: $i] : (m2_relset_1(C, B, A) => ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k10_relset_1(A, B, k6_relset_1(B, A, C), k10_relset_1(B, A, C, B)) = k10_relset_1(A, B, k6_relset_1(B, A, C), k2_funct_5(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t56_relset_2')).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k10_relset_1(A, B, k6_relset_1(B, A, C), k10_relset_1(B, A, C, B)) = k10_relset_1(A, B, k6_relset_1(B, A, C), k2_funct_5(C)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k10_relset_1(A, B, k6_relset_1(B, A, C), k10_relset_1(B, A, C, B)) = k10_relset_1(A, B, k6_relset_1(B, A, C), k2_funct_5(C)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 14])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k10_relset_1(A, B, k6_relset_1(B, A, C), k10_relset_1(B, A, C, B)) = k10_relset_1(A, B, k6_relset_1(B, A, C), k2_funct_5(C)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 (~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | ((k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A)) & (k10_relset_1(A, B, k6_relset_1(B, A, C), k10_relset_1(B, A, C, B)) = k10_relset_1(A, B, k6_relset_1(B, A, C), k2_funct_5(C)))))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.20/0.38 tff(21,plain,(
% 0.20/0.38 ~((~m2_relset_1(C!0, B!1, A!2)) | ((k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2)) & (k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0)))))),
% 0.20/0.38 inference(skolemize,[status(sab)],[20])).
% 0.20/0.38 tff(22,plain,
% 0.20/0.38 (m2_relset_1(C!0, B!1, A!2)),
% 0.20/0.38 inference(or_elim,[status(thm)],[21])).
% 0.20/0.38 tff(23,plain,
% 0.20/0.38 (((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | (~((~(k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A))) | (~(k2_funct_5(C) = k10_relset_1(B, A, C, B))))))) | ((~m2_relset_1(C!0, B!1, A!2)) | (~((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k2_funct_5(C!0) = k10_relset_1(B!1, A!2, C!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | (~((~(k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A))) | (~(k2_funct_5(C) = k10_relset_1(B, A, C, B))))))) | (~m2_relset_1(C!0, B!1, A!2)) | (~((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k2_funct_5(C!0) = k10_relset_1(B!1, A!2, C!0, B!1))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | (~((~(k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A))) | (~(k2_funct_5(C) = k10_relset_1(B, A, C, B))))))) | ((~m2_relset_1(C!0, B!1, A!2)) | (~((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k2_funct_5(C!0) = k10_relset_1(B!1, A!2, C!0, B!1))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 ((~![A: $i, B: $i, C: $i] : ((~m2_relset_1(C, B, A)) | (~((~(k1_funct_5(C) = k10_relset_1(A, B, k6_relset_1(B, A, C), A))) | (~(k2_funct_5(C) = k10_relset_1(B, A, C, B))))))) | (~m2_relset_1(C!0, B!1, A!2)) | (~((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k2_funct_5(C!0) = k10_relset_1(B!1, A!2, C!0, B!1)))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (~((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k2_funct_5(C!0) = k10_relset_1(B!1, A!2, C!0, B!1))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[25, 22, 13])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k2_funct_5(C!0) = k10_relset_1(B!1, A!2, C!0, B!1)))) | (k2_funct_5(C!0) = k10_relset_1(B!1, A!2, C!0, B!1))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (k2_funct_5(C!0) = k10_relset_1(B!1, A!2, C!0, B!1)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[28])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0))),
% 0.20/0.39 inference(symmetry,[status(thm)],[29])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k2_funct_5(C!0) = k10_relset_1(B!1, A!2, C!0, B!1)))) | (k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))),
% 0.20/0.39 inference(tautology,[status(thm)],[])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[31, 26])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 ((~(~((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0))))))) <=> ((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (((k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2)) & (k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0)))) <=> (~((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 ((~((k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2)) & (k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0))))) <=> (~(~((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0)))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[34])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 ((~((k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2)) & (k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0))))) <=> ((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[35, 33])).
% 0.20/0.39 tff(37,plain,
% 0.20/0.39 (~((k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2)) & (k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0))))),
% 0.20/0.39 inference(or_elim,[status(thm)],[21])).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 ((~(k1_funct_5(C!0) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), A!2))) | (~(k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (~(k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k10_relset_1(B!1, A!2, C!0, B!1)) = k10_relset_1(A!2, B!1, k6_relset_1(B!1, A!2, C!0), k2_funct_5(C!0)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[38, 32])).
% 0.20/0.39 tff(40,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[39, 30])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------