%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN587-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:39:38 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN587-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n015.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 12:38:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(p2_type, type, (
% 0.20/0.38 p2: ( $i * $i ) > $o)).
% 0.20/0.38 tff(c20_type, type, (
% 0.20/0.38 c20: $i)).
% 0.20/0.38 tff(f4_type, type, (
% 0.20/0.38 f4: ( $i * $i ) > $i)).
% 0.20/0.38 tff(c21_type, type, (
% 0.20/0.38 c21: $i)).
% 0.20/0.38 tff(f6_type, type, (
% 0.20/0.38 f6: ( $i * $i ) > $i)).
% 0.20/0.38 tff(c18_type, type, (
% 0.20/0.38 c18: $i)).
% 0.20/0.38 tff(f7_type, type, (
% 0.20/0.38 f7: $i > $i)).
% 0.20/0.38 tff(f8_type, type, (
% 0.20/0.38 f8: $i > $i)).
% 0.20/0.38 tff(f9_type, type, (
% 0.20/0.38 f9: $i > $i)).
% 0.20/0.38 tff(c17_type, type, (
% 0.20/0.38 c17: $i)).
% 0.20/0.38 tff(f10_type, type, (
% 0.20/0.38 f10: $i > $i)).
% 0.20/0.38 tff(c16_type, type, (
% 0.20/0.38 c16: $i)).
% 0.20/0.38 tff(c19_type, type, (
% 0.20/0.38 c19: $i)).
% 0.20/0.38 tff(p3_type, type, (
% 0.20/0.38 p3: ( $i * $i ) > $o)).
% 0.20/0.38 tff(p15_type, type, (
% 0.20/0.38 p15: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,assumption,(~p2(c20, c20)), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[X13: $i] : refl(p2(X13, X13) <=> p2(X13, X13))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![X13: $i] : p2(X13, X13) <=> ![X13: $i] : p2(X13, X13)),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![X13: $i] : p2(X13, X13) <=> ![X13: $i] : p2(X13, X13)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,axiom,(![X13: $i] : p2(X13, X13)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_4')).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (![X13: $i] : p2(X13, X13)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,(
% 0.20/0.38 ![X13: $i] : p2(X13, X13)),
% 0.20/0.38 inference(skolemize,[status(sab)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![X13: $i] : p2(X13, X13)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ((~![X13: $i] : p2(X13, X13)) | p2(c20, c20)),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.38 tff(11,plain,(p2(c20, c20)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(12,assumption,(~p3(c21, c21)), introduced(assumption)).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (^[X24: $i] : refl(p3(X24, X24) <=> p3(X24, X24))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![X24: $i] : p3(X24, X24) <=> ![X24: $i] : p3(X24, X24)),
% 0.20/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (![X24: $i] : p3(X24, X24) <=> ![X24: $i] : p3(X24, X24)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(16,axiom,(![X24: $i] : p3(X24, X24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_3')).
% 0.20/0.38 tff(17,plain,
% 0.20/0.38 (![X24: $i] : p3(X24, X24)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.38 tff(18,plain,(
% 0.20/0.38 ![X24: $i] : p3(X24, X24)),
% 0.20/0.38 inference(skolemize,[status(sab)],[17])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![X24: $i] : p3(X24, X24)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.38 tff(20,plain,
% 0.20/0.38 ((~![X24: $i] : p3(X24, X24)) | p3(c21, c21)),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(21,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 0.20/0.38 tff(22,plain,(p3(c21, c21)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(23,assumption,(~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))), introduced(assumption)).
% 0.20/0.38 tff(24,plain,
% 0.20/0.38 ((~![X13: $i] : p2(X13, X13)) | p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(25,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[24, 8, 23])).
% 0.20/0.38 tff(26,plain,(p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(27,plain,
% 0.20/0.38 (^[X17: $i, X16: $i, X18: $i, X19: $i] : refl(((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19))) <=> ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(28,plain,
% 0.20/0.38 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19))) <=> ![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.38 tff(29,plain,
% 0.20/0.38 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19))) <=> ![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(30,plain,
% 0.20/0.38 (^[X17: $i, X16: $i, X18: $i, X19: $i] : trans(monotonicity(rewrite((p2(f4(X16, X17), f4(X18, X19)) | (~p2(X16, X18))) <=> ((~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))), (((p2(f4(X16, X17), f4(X18, X19)) | (~p2(X16, X18))) | (~p3(X17, X19))) <=> (((~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19))) | (~p3(X17, X19))))), rewrite((((~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19))) | (~p3(X17, X19))) <=> ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))), (((p2(f4(X16, X17), f4(X18, X19)) | (~p2(X16, X18))) | (~p3(X17, X19))) <=> ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(31,plain,
% 0.20/0.38 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((p2(f4(X16, X17), f4(X18, X19)) | (~p2(X16, X18))) | (~p3(X17, X19))) <=> ![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.38 tff(32,axiom,(![X17: $i, X16: $i, X18: $i, X19: $i] : ((p2(f4(X16, X17), f4(X18, X19)) | (~p2(X16, X18))) | (~p3(X17, X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_20')).
% 0.20/0.38 tff(33,plain,
% 0.20/0.38 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.38 tff(34,plain,
% 0.20/0.38 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.20/0.38 tff(35,plain,(
% 0.20/0.38 ![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[34])).
% 0.20/0.38 tff(36,plain,
% 0.20/0.38 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.20/0.38 tff(37,plain,
% 0.20/0.38 (((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))) | ((~p3(c21, c21)) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)))) <=> ((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))) | (~p3(c21, c21)) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(38,plain,
% 0.20/0.38 ((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))) | ((~p3(c21, c21)) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(39,plain,
% 0.20/0.38 ((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))) | (~p3(c21, c21)) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.38 tff(40,plain,
% 0.20/0.38 ((~p3(c21, c21)) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[39, 36])).
% 0.20/0.38 tff(41,plain,
% 0.20/0.38 ((~p3(c21, c21)) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[40, 26])).
% 0.20/0.38 tff(42,plain,
% 0.20/0.38 (p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[41, 22])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (p3(c21, c19) <=> p3(c21, c19)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(44,axiom,(p3(c21, c19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_5')).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (p3(c21, c19)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 (((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))) | ((~p3(c21, c19)) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19)))) <=> ((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))) | (~p3(c21, c19)) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 ((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))) | ((~p3(c21, c19)) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p3(X17, X19)) | (~p2(X16, X18)) | p2(f4(X16, X17), f4(X18, X19)))) | (~p3(c21, c19)) | (~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 ((~p2(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), f6(f10(c16), f6(f7(f8(f9(c17))), c18)))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[48, 45, 36])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[49, 26])).
% 0.20/0.39 tff(51,plain,
% 0.20/0.39 (^[X14: $i, X13: $i, X15: $i] : refl(((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15)) <=> ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15)) <=> ![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15)) <=> ![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 (^[X14: $i, X13: $i, X15: $i] : trans(monotonicity(rewrite((p2(X14, X15) | (~p2(X13, X14))) <=> ((~p2(X13, X14)) | p2(X14, X15))), (((p2(X14, X15) | (~p2(X13, X14))) | (~p2(X13, X15))) <=> (((~p2(X13, X14)) | p2(X14, X15)) | (~p2(X13, X15))))), rewrite((((~p2(X13, X14)) | p2(X14, X15)) | (~p2(X13, X15))) <=> ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))), (((p2(X14, X15) | (~p2(X13, X14))) | (~p2(X13, X15))) <=> ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 (![X14: $i, X13: $i, X15: $i] : ((p2(X14, X15) | (~p2(X13, X14))) | (~p2(X13, X15))) <=> ![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.39 tff(56,axiom,(![X14: $i, X13: $i, X15: $i] : ((p2(X14, X15) | (~p2(X13, X14))) | (~p2(X13, X15)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_16')).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.39 tff(59,plain,(
% 0.20/0.39 ![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))),
% 0.20/0.39 inference(skolemize,[status(sab)],[58])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (((~![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))) | (p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))))) <=> ((~![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(62,plain,
% 0.20/0.39 (((~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) <=> (p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (((~![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))) | ((~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)))) <=> ((~![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))) | (p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (((~![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))) | ((~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)))) <=> ((~![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.39 tff(65,plain,
% 0.20/0.39 ((~![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))) | ((~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 ((~![X14: $i, X13: $i, X15: $i] : ((~p2(X13, X15)) | (~p2(X13, X14)) | p2(X14, X15))) | p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19))) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[66, 60, 50, 42])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 ((~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20)) <=> (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(69,axiom,(~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p15_19')).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20) <=> p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(72,axiom,(p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p15_18')).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (^[X9: $i, X12: $i, X11: $i, X10: $i] : refl(((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)) <=> ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (^[X9: $i, X12: $i, X11: $i, X10: $i] : trans(monotonicity(trans(monotonicity(rewrite((p15(X9, X10) | (~p2(X11, X9))) <=> ((~p2(X11, X9)) | p15(X9, X10))), (((p15(X9, X10) | (~p2(X11, X9))) | (~p2(X12, X10))) <=> (((~p2(X11, X9)) | p15(X9, X10)) | (~p2(X12, X10))))), rewrite((((~p2(X11, X9)) | p15(X9, X10)) | (~p2(X12, X10))) <=> ((~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))), (((p15(X9, X10) | (~p2(X11, X9))) | (~p2(X12, X10))) <=> ((~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)))), ((((p15(X9, X10) | (~p2(X11, X9))) | (~p2(X12, X10))) | (~p15(X11, X12))) <=> (((~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)) | (~p15(X11, X12))))), rewrite((((~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10)) | (~p15(X11, X12))) <=> ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))), ((((p15(X9, X10) | (~p2(X11, X9))) | (~p2(X12, X10))) | (~p15(X11, X12))) <=> ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i] : (((p15(X9, X10) | (~p2(X11, X9))) | (~p2(X12, X10))) | (~p15(X11, X12))) <=> ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.40 tff(79,axiom,(![X9: $i, X12: $i, X11: $i, X10: $i] : (((p15(X9, X10) | (~p2(X11, X9))) | (~p2(X12, X10))) | (~p15(X11, X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p15_17')).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.40 tff(82,plain,(
% 0.20/0.40 ![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.20/0.40 inference(skolemize,[status(sab)],[81])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | (p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | (~p2(c20, c20)) | (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20)))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | (~p2(c20, c20)) | (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(85,plain,
% 0.20/0.40 (((~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20)) | (~p2(c20, c20)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20)) <=> (p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | (~p2(c20, c20)) | (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | ((~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20)) | (~p2(c20, c20)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | (p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | (~p2(c20, c20)) | (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[85])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | ((~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20)) | (~p2(c20, c20)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20))) <=> ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | (~p2(c20, c20)) | (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20)))),
% 0.20/0.40 inference(transitivity,[status(thm)],[86, 84])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | ((~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20)) | (~p2(c20, c20)) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 ((~![X9: $i, X12: $i, X11: $i, X10: $i] : ((~p15(X11, X12)) | (~p2(X12, X10)) | (~p2(X11, X9)) | p15(X9, X10))) | p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21), c20) | (~p2(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c21))) | (~p2(c20, c20)) | (~p15(f4(f6(f10(c16), f6(f7(f8(f9(c17))), c18)), c19), c20))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[89, 83, 73, 70, 67, 11])).
% 0.20/0.40 % SZS output end Proof
% 0.20/0.40 % E exiting
%------------------------------------------------------------------------------