%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO578+1 : TPTP v9.0.0. Released v5.5.0.
% 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 05:41:54 AM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO578+1 : TPTP v9.0.0. Released v5.5.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n009.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 : Fri Jun 20 13:11:33 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 tff(b48_buttercup10098_type, type, (
% 0.20/0.41 b48_buttercup10098: $i > $o)).
% 0.20/0.41 tff(k04_buttercup10100_type, type, (
% 0.20/0.41 k04_buttercup10100: $i > $o)).
% 0.20/0.41 tff(tptp_fun_X144_56_type, type, (
% 0.20/0.41 tptp_fun_X144_56: $i)).
% 0.20/0.41 tff(tptp_fun_X18_5_type, type, (
% 0.20/0.41 tptp_fun_X18_5: $i)).
% 0.20/0.41 tff(b48_buttercup10109_type, type, (
% 0.20/0.41 b48_buttercup10109: $i > $o)).
% 0.20/0.41 tff(tptp_fun_X62_31_type, type, (
% 0.20/0.41 tptp_fun_X62_31: $i)).
% 0.20/0.41 tff(1,plain,
% 0.20/0.41 (^[X61: $i] : refl((b48_buttercup10098(X61) | (~k04_buttercup10100(X61))) <=> (b48_buttercup10098(X61) | (~k04_buttercup10100(X61))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(2,plain,
% 0.20/0.41 (![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61))) <=> ![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.41 tff(3,plain,
% 0.20/0.41 (![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61))) <=> ![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(4,plain,
% 0.20/0.41 (^[X61: $i] : rewrite((k04_buttercup10100(X61) => b48_buttercup10098(X61)) <=> (b48_buttercup10098(X61) | (~k04_buttercup10100(X61))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(5,plain,
% 0.20/0.41 (![X61: $i] : (k04_buttercup10100(X61) => b48_buttercup10098(X61)) <=> ![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.41 tff(6,axiom,(![X61: $i] : (k04_buttercup10100(X61) => b48_buttercup10098(X61)) & ?[X62: $i] : (b48_buttercup10098(X62) & (~k04_buttercup10100(X62)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_21')).
% 0.20/0.41 tff(7,plain,
% 0.20/0.41 (![X61: $i] : (k04_buttercup10100(X61) => b48_buttercup10098(X61))),
% 0.20/0.41 inference(and_elim,[status(thm)],[6])).
% 0.20/0.41 tff(8,plain,
% 0.20/0.41 (![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[7, 5])).
% 0.20/0.41 tff(9,plain,
% 0.20/0.41 (![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.20/0.41 tff(10,plain,(
% 0.20/0.41 ![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[9])).
% 0.20/0.41 tff(11,plain,
% 0.20/0.41 (![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.20/0.41 tff(12,plain,
% 0.20/0.41 (?[X18: $i] : (k04_buttercup10100(X18) & (~b48_buttercup10109(X18))) <=> ?[X18: $i] : (k04_buttercup10100(X18) & (~b48_buttercup10109(X18)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(13,axiom,(![X17: $i] : (b48_buttercup10109(X17) => k04_buttercup10100(X17)) & ?[X18: $i] : (k04_buttercup10100(X18) & (~b48_buttercup10109(X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sos_11')).
% 0.20/0.41 tff(14,plain,
% 0.20/0.41 (?[X18: $i] : (k04_buttercup10100(X18) & (~b48_buttercup10109(X18)))),
% 0.20/0.41 inference(and_elim,[status(thm)],[13])).
% 0.20/0.41 tff(15,plain,
% 0.20/0.41 (?[X18: $i] : (k04_buttercup10100(X18) & (~b48_buttercup10109(X18)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.20/0.41 tff(16,plain,(
% 0.20/0.41 k04_buttercup10100(X18!5) & (~b48_buttercup10109(X18!5))),
% 0.20/0.41 inference(skolemize,[status(sab)],[15])).
% 0.20/0.41 tff(17,plain,
% 0.20/0.41 (k04_buttercup10100(X18!5)),
% 0.20/0.41 inference(and_elim,[status(thm)],[16])).
% 0.20/0.41 tff(18,plain,
% 0.20/0.41 (((~![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61)))) | (b48_buttercup10098(X18!5) | (~k04_buttercup10100(X18!5)))) <=> ((~![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61)))) | b48_buttercup10098(X18!5) | (~k04_buttercup10100(X18!5)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(19,plain,
% 0.20/0.41 ((~![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61)))) | (b48_buttercup10098(X18!5) | (~k04_buttercup10100(X18!5)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(20,plain,
% 0.20/0.41 ((~![X61: $i] : (b48_buttercup10098(X61) | (~k04_buttercup10100(X61)))) | b48_buttercup10098(X18!5) | (~k04_buttercup10100(X18!5))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.41 tff(21,plain,
% 0.20/0.41 (b48_buttercup10098(X18!5)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[20, 17, 11])).
% 0.20/0.41 tff(22,plain,
% 0.20/0.41 (^[X146: $i, X147: $i, X148: $i] : refl((k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147))) <=> (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(23,plain,
% 0.20/0.41 (![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147))) <=> ![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.41 tff(24,plain,
% 0.20/0.41 (^[X146: $i, X147: $i, X148: $i] : trans(monotonicity(rewrite((k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148)) <=> (~(k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147))))), ((~(k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148))) <=> (~(~(k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147))))))), rewrite((~(~(k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147))))) <=> (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))), ((~(k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148))) <=> (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(25,plain,
% 0.20/0.41 (![X146: $i, X147: $i, X148: $i] : (~(k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148))) <=> ![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.41 tff(26,plain,
% 0.20/0.41 ((~?[X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148))) <=> (~?[X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(27,plain,
% 0.20/0.41 ((~?[X146: $i, X147: $i, X148: $i] : (((((k04_buttercup10100(X146) & b48_buttercup10098(X146)) & k04_buttercup10100(X147)) & (~b48_buttercup10098(X147))) & (~k04_buttercup10100(X148))) & b48_buttercup10098(X148))) <=> (~?[X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(28,axiom,(~((((![X142: $i] : (b48_buttercup10098(X142) => k04_buttercup10100(X142)) & ?[X143: $i] : (k04_buttercup10100(X143) & (~b48_buttercup10098(X143)))) | (![X144: $i] : (k04_buttercup10100(X144) => b48_buttercup10098(X144)) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))) | ?[X146: $i, X147: $i, X148: $i] : (((((k04_buttercup10100(X146) & b48_buttercup10098(X146)) & k04_buttercup10100(X147)) & (~b48_buttercup10098(X147))) & (~k04_buttercup10100(X148))) & b48_buttercup10098(X148))) | ![X149: $i] : (k04_buttercup10100(X149) => (~b48_buttercup10098(X149))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals_86')).
% 0.20/0.41 tff(29,plain,
% 0.20/0.41 (~(((![X142: $i] : (b48_buttercup10098(X142) => k04_buttercup10100(X142)) & ?[X143: $i] : (k04_buttercup10100(X143) & (~b48_buttercup10098(X143)))) | (![X144: $i] : (k04_buttercup10100(X144) => b48_buttercup10098(X144)) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))) | ?[X146: $i, X147: $i, X148: $i] : (((((k04_buttercup10100(X146) & b48_buttercup10098(X146)) & k04_buttercup10100(X147)) & (~b48_buttercup10098(X147))) & (~k04_buttercup10100(X148))) & b48_buttercup10098(X148)))),
% 0.20/0.41 inference(or_elim,[status(thm)],[28])).
% 0.20/0.41 tff(30,plain,
% 0.20/0.41 (~?[X146: $i, X147: $i, X148: $i] : (((((k04_buttercup10100(X146) & b48_buttercup10098(X146)) & k04_buttercup10100(X147)) & (~b48_buttercup10098(X147))) & (~k04_buttercup10100(X148))) & b48_buttercup10098(X148))),
% 0.20/0.41 inference(or_elim,[status(thm)],[29])).
% 0.20/0.41 tff(31,plain,
% 0.20/0.41 (~?[X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.20/0.41 tff(32,plain,
% 0.20/0.41 (~?[X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.20/0.41 tff(33,plain,
% 0.20/0.41 (~?[X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.20/0.41 tff(34,plain,
% 0.20/0.41 (~?[X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.20/0.41 tff(35,plain,
% 0.20/0.41 (^[X146: $i, X147: $i, X148: $i] : refl($oeq((~(k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148))), (~(k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(36,plain,(
% 0.20/0.41 ![X146: $i, X147: $i, X148: $i] : (~(k04_buttercup10100(X146) & b48_buttercup10098(X146) & k04_buttercup10100(X147) & (~b48_buttercup10098(X147)) & (~k04_buttercup10100(X148)) & b48_buttercup10098(X148)))),
% 0.20/0.41 inference(nnf-neg,[status(sab)],[34, 35])).
% 0.20/0.41 tff(37,plain,
% 0.20/0.41 (![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[36, 25])).
% 0.20/0.41 tff(38,plain,
% 0.20/0.41 (![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[37, 23])).
% 0.20/0.41 tff(39,assumption,(~(b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)))), introduced(assumption)).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 ((b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56))) | k04_buttercup10100(X144!56)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(41,plain,
% 0.20/0.41 (k04_buttercup10100(X144!56)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 ((b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56))) | (~b48_buttercup10098(X144!56))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (~b48_buttercup10098(X144!56)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[42, 39])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 (?[X62: $i] : (b48_buttercup10098(X62) & (~k04_buttercup10100(X62))) <=> ?[X62: $i] : (b48_buttercup10098(X62) & (~k04_buttercup10100(X62)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 (?[X62: $i] : (b48_buttercup10098(X62) & (~k04_buttercup10100(X62)))),
% 0.20/0.42 inference(and_elim,[status(thm)],[6])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (?[X62: $i] : (b48_buttercup10098(X62) & (~k04_buttercup10100(X62)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.20/0.42 tff(47,plain,(
% 0.20/0.42 b48_buttercup10098(X62!31) & (~k04_buttercup10100(X62!31))),
% 0.20/0.42 inference(skolemize,[status(sab)],[46])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (~k04_buttercup10100(X62!31)),
% 0.20/0.42 inference(and_elim,[status(thm)],[47])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (b48_buttercup10098(X62!31)),
% 0.20/0.42 inference(and_elim,[status(thm)],[47])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (((~![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))) | (k04_buttercup10100(X62!31) | b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)) | (~b48_buttercup10098(X62!31)) | (~b48_buttercup10098(X18!5)) | (~k04_buttercup10100(X18!5)))) <=> ((~![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))) | k04_buttercup10100(X62!31) | b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)) | (~b48_buttercup10098(X62!31)) | (~b48_buttercup10098(X18!5)) | (~k04_buttercup10100(X18!5)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 ((k04_buttercup10100(X62!31) | (~b48_buttercup10098(X62!31)) | b48_buttercup10098(X144!56) | (~k04_buttercup10100(X18!5)) | (~b48_buttercup10098(X18!5)) | (~k04_buttercup10100(X144!56))) <=> (k04_buttercup10100(X62!31) | b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)) | (~b48_buttercup10098(X62!31)) | (~b48_buttercup10098(X18!5)) | (~k04_buttercup10100(X18!5)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (((~![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))) | (k04_buttercup10100(X62!31) | (~b48_buttercup10098(X62!31)) | b48_buttercup10098(X144!56) | (~k04_buttercup10100(X18!5)) | (~b48_buttercup10098(X18!5)) | (~k04_buttercup10100(X144!56)))) <=> ((~![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))) | (k04_buttercup10100(X62!31) | b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)) | (~b48_buttercup10098(X62!31)) | (~b48_buttercup10098(X18!5)) | (~k04_buttercup10100(X18!5))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 (((~![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))) | (k04_buttercup10100(X62!31) | (~b48_buttercup10098(X62!31)) | b48_buttercup10098(X144!56) | (~k04_buttercup10100(X18!5)) | (~b48_buttercup10098(X18!5)) | (~k04_buttercup10100(X144!56)))) <=> ((~![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))) | k04_buttercup10100(X62!31) | b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)) | (~b48_buttercup10098(X62!31)) | (~b48_buttercup10098(X18!5)) | (~k04_buttercup10100(X18!5)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[52, 50])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 ((~![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))) | (k04_buttercup10100(X62!31) | (~b48_buttercup10098(X62!31)) | b48_buttercup10098(X144!56) | (~k04_buttercup10100(X18!5)) | (~b48_buttercup10098(X18!5)) | (~k04_buttercup10100(X144!56)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 ((~![X146: $i, X147: $i, X148: $i] : (k04_buttercup10100(X148) | (~b48_buttercup10098(X148)) | b48_buttercup10098(X147) | (~k04_buttercup10100(X146)) | (~b48_buttercup10098(X146)) | (~k04_buttercup10100(X147)))) | k04_buttercup10100(X62!31) | b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)) | (~b48_buttercup10098(X62!31)) | (~b48_buttercup10098(X18!5)) | (~k04_buttercup10100(X18!5))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[55, 17, 49, 48, 43, 41, 38, 21])).
% 0.20/0.42 tff(57,plain,(b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (((~(b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)))) | ![X145: $i] : (k04_buttercup10100(X145) | (~b48_buttercup10098(X145)))) <=> ((~(b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)))) | ![X145: $i] : (k04_buttercup10100(X145) | (~b48_buttercup10098(X145))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (((~(b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)))) | ![X145: $i] : (~(b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))) <=> ((~(b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)))) | ![X145: $i] : (k04_buttercup10100(X145) | (~b48_buttercup10098(X145))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (((~(b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)))) | ![X145: $i] : (~(b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))) <=> ((~(b48_buttercup10098(X144!56) | (~k04_buttercup10100(X144!56)))) | ![X145: $i] : (~(b48_buttercup10098(X145) & (~k04_buttercup10100(X145)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 ((![X144: $i] : (b48_buttercup10098(X144) | (~k04_buttercup10100(X144))) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145)))) <=> (![X144: $i] : (b48_buttercup10098(X144) | (~k04_buttercup10100(X144))) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 ((~(![X144: $i] : (b48_buttercup10098(X144) | (~k04_buttercup10100(X144))) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))) <=> (~(![X144: $i] : (b48_buttercup10098(X144) | (~k04_buttercup10100(X144))) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145)))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 ((~(![X144: $i] : (b48_buttercup10098(X144) | (~k04_buttercup10100(X144))) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))) <=> (~(![X144: $i] : (b48_buttercup10098(X144) | (~k04_buttercup10100(X144))) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 ((~(![X144: $i] : (k04_buttercup10100(X144) => b48_buttercup10098(X144)) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))) <=> (~(![X144: $i] : (b48_buttercup10098(X144) | (~k04_buttercup10100(X144))) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(65,plain,
% 0.20/0.42 (~((![X142: $i] : (b48_buttercup10098(X142) => k04_buttercup10100(X142)) & ?[X143: $i] : (k04_buttercup10100(X143) & (~b48_buttercup10098(X143)))) | (![X144: $i] : (k04_buttercup10100(X144) => b48_buttercup10098(X144)) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145)))))),
% 0.20/0.42 inference(or_elim,[status(thm)],[29])).
% 0.20/0.42 tff(66,plain,
% 0.20/0.42 (~(![X144: $i] : (k04_buttercup10100(X144) => b48_buttercup10098(X144)) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))),
% 0.20/0.42 inference(or_elim,[status(thm)],[65])).
% 0.20/0.42 tff(67,plain,
% 0.20/0.42 (~(![X144: $i] : (b48_buttercup10098(X144) | (~k04_buttercup10100(X144))) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[66, 64])).
% 0.20/0.42 tff(68,plain,
% 0.20/0.42 (~(![X144: $i] : (b48_buttercup10098(X144) | (~k04_buttercup10100(X144))) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[67, 62])).
% 0.20/0.42 tff(69,plain,
% 0.20/0.42 (~(![X144: $i] : (b48_buttercup10098(X144) | (~k04_buttercup10100(X144))) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[68, 63])).
% 0.20/0.42 tff(70,plain,
% 0.20/0.42 (~(![X144: $i] : (b48_buttercup10098(X144) | (~k04_buttercup10100(X144))) & ?[X145: $i] : (b48_buttercup10098(X145) & (~k04_buttercup10100(X145))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.20/0.42 unexpected number of arguments: (let ((a!1 (forall ((X144 $i))
% 0.20/0.42 (or (b48_buttercup10098 X144) (not (k04_buttercup10100 X144)))))
% 0.20/0.42 (a!2 (not (or (b48_buttercup10098 X144!56)
% 0.20/0.42 (not (k04_buttercup10100 X144!56)))))
% 0.20/0.42 (a!3 (proof-bind (lambda ((X145 $i))
% 0.20/0.42 (let ((a!1 (not (and (b48_buttercup10098 X145)
% 0.20/0.42 (not (k04_buttercup10100 X145))))))
% 0.20/0.42 (refl (~ a!1 a!1))))))
% 0.20/0.42 (a!4 (exists ((X145 $i))
% 0.20/0.42 (and (b48_buttercup10098 X145) (not (k04_buttercup10100 X145)))))
% 0.20/0.42 (a!5 (forall ((X145 $i))
% 0.20/0.42 (not (and (b48_buttercup10098 X145)
% 0.20/0.42 (not (k04_buttercup10100 X145)))))))
% 0.20/0.42 (nnf-neg (sk (~ (not a!1) a!2))
% 0.20/0.42 (nnf-neg a!3 (~ (not a!4) a!5))
% 0.20/0.42 (~ (not (and a!1 a!4)) (or a!2 a!5))))
% 0.20/0.42 Proof display could not be completed: unexpected number of arguments
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------