%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN627-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:39:43 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.50s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN627-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:38:37 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.21/0.50 % SZS status Unsatisfiable
% 0.21/0.50 % SZS output start Proof
% 0.21/0.50 tff(p3_type, type, (
% 0.21/0.50 p3: ( $i * $i ) > $o)).
% 0.21/0.50 tff(c24_type, type, (
% 0.21/0.50 c24: $i)).
% 0.21/0.50 tff(f4_type, type, (
% 0.21/0.50 f4: ( $i * $i ) > $i)).
% 0.21/0.50 tff(f14_type, type, (
% 0.21/0.50 f14: $i > $i)).
% 0.21/0.50 tff(c18_type, type, (
% 0.21/0.50 c18: $i)).
% 0.21/0.50 tff(f7_type, type, (
% 0.21/0.50 f7: ( $i * $i ) > $i)).
% 0.21/0.50 tff(c17_type, type, (
% 0.21/0.50 c17: $i)).
% 0.21/0.50 tff(p15_type, type, (
% 0.21/0.50 p15: ( $i * $i ) > $o)).
% 0.21/0.50 tff(c19_type, type, (
% 0.21/0.50 c19: $i)).
% 0.21/0.50 tff(c23_type, type, (
% 0.21/0.50 c23: $i)).
% 0.21/0.50 tff(f13_type, type, (
% 0.21/0.50 f13: $i > $i)).
% 0.21/0.50 tff(p2_type, type, (
% 0.21/0.50 p2: ( $i * $i ) > $o)).
% 0.21/0.50 tff(p16_type, type, (
% 0.21/0.50 p16: ( $i * $i * $i * $i * $i ) > $o)).
% 0.21/0.50 tff(c22_type, type, (
% 0.21/0.50 c22: $i)).
% 0.21/0.50 tff(f9_type, type, (
% 0.21/0.50 f9: ( $i * $i ) > $i)).
% 0.21/0.50 tff(c20_type, type, (
% 0.21/0.50 c20: $i)).
% 0.21/0.50 tff(c25_type, type, (
% 0.21/0.50 c25: $i)).
% 0.21/0.50 tff(1,plain,
% 0.21/0.50 (^[X40: $i] : refl(p3(X40, X40) <=> p3(X40, X40))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(2,plain,
% 0.21/0.50 (![X40: $i] : p3(X40, X40) <=> ![X40: $i] : p3(X40, X40)),
% 0.21/0.50 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.50 tff(3,plain,
% 0.21/0.50 (![X40: $i] : p3(X40, X40) <=> ![X40: $i] : p3(X40, X40)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(4,axiom,(![X40: $i] : p3(X40, X40)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_5')).
% 0.21/0.50 tff(5,plain,
% 0.21/0.50 (![X40: $i] : p3(X40, X40)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.50 tff(6,plain,(
% 0.21/0.50 ![X40: $i] : p3(X40, X40)),
% 0.21/0.50 inference(skolemize,[status(sab)],[5])).
% 0.21/0.50 tff(7,plain,
% 0.21/0.50 (![X40: $i] : p3(X40, X40)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.50 tff(8,plain,
% 0.21/0.50 ((~![X40: $i] : p3(X40, X40)) | p3(c24, c24)),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(9,plain,
% 0.21/0.50 (p3(c24, c24)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.50 tff(10,plain,
% 0.21/0.50 (^[X32: $i] : refl(((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32)))) <=> ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(11,plain,
% 0.21/0.50 (![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32)))) <=> ![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.50 tff(12,plain,
% 0.21/0.50 (![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32)))) <=> ![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(13,plain,
% 0.21/0.50 (^[X32: $i] : rewrite((p3(c24, f4(f7(c17, X32), f14(X32))) | (~p15(X32, c19))) <=> ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32)))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(14,plain,
% 0.21/0.50 (![X32: $i] : (p3(c24, f4(f7(c17, X32), f14(X32))) | (~p15(X32, c19))) <=> ![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32))))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.50 tff(15,axiom,(![X32: $i] : (p3(c24, f4(f7(c17, X32), f14(X32))) | (~p15(X32, c19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_20')).
% 0.21/0.50 tff(16,plain,
% 0.21/0.50 (![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.50 tff(17,plain,
% 0.21/0.50 (![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.21/0.50 tff(18,plain,(
% 0.21/0.50 ![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32))))),
% 0.21/0.50 inference(skolemize,[status(sab)],[17])).
% 0.21/0.50 tff(19,plain,
% 0.21/0.50 (![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32))))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.21/0.50 tff(20,plain,
% 0.21/0.50 (p15(c18, c19) <=> p15(c18, c19)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(21,axiom,(p15(c18, c19)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p15_7')).
% 0.21/0.50 tff(22,plain,
% 0.21/0.50 (p15(c18, c19)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.50 tff(23,plain,
% 0.21/0.50 (((~![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32))))) | ((~p15(c18, c19)) | p3(c24, f4(f7(c17, c18), f14(c18))))) <=> ((~![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32))))) | (~p15(c18, c19)) | p3(c24, f4(f7(c17, c18), f14(c18))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(24,plain,
% 0.21/0.50 ((~![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32))))) | ((~p15(c18, c19)) | p3(c24, f4(f7(c17, c18), f14(c18))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(25,plain,
% 0.21/0.50 ((~![X32: $i] : ((~p15(X32, c19)) | p3(c24, f4(f7(c17, X32), f14(X32))))) | (~p15(c18, c19)) | p3(c24, f4(f7(c17, c18), f14(c18)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.50 tff(26,plain,
% 0.21/0.50 (p3(c24, f4(f7(c17, c18), f14(c18)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[25, 22, 19])).
% 0.21/0.50 tff(27,plain,
% 0.21/0.50 (^[X42: $i, X41: $i, X40: $i] : refl(((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42)) <=> ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(28,plain,
% 0.21/0.50 (![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42)) <=> ![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[27])).
% 0.21/0.50 tff(29,plain,
% 0.21/0.50 (![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42)) <=> ![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(30,plain,
% 0.21/0.50 (^[X42: $i, X41: $i, X40: $i] : trans(monotonicity(rewrite((p3(X41, X42) | (~p3(X40, X41))) <=> ((~p3(X40, X41)) | p3(X41, X42))), (((p3(X41, X42) | (~p3(X40, X41))) | (~p3(X40, X42))) <=> (((~p3(X40, X41)) | p3(X41, X42)) | (~p3(X40, X42))))), rewrite((((~p3(X40, X41)) | p3(X41, X42)) | (~p3(X40, X42))) <=> ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))), (((p3(X41, X42) | (~p3(X40, X41))) | (~p3(X40, X42))) <=> ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(31,plain,
% 0.21/0.50 (![X42: $i, X41: $i, X40: $i] : ((p3(X41, X42) | (~p3(X40, X41))) | (~p3(X40, X42))) <=> ![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[30])).
% 0.21/0.50 tff(32,axiom,(![X42: $i, X41: $i, X40: $i] : ((p3(X41, X42) | (~p3(X40, X41))) | (~p3(X40, X42)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_18')).
% 0.21/0.50 tff(33,plain,
% 0.21/0.50 (![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.21/0.50 tff(34,plain,
% 0.21/0.50 (![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.21/0.50 tff(35,plain,(
% 0.21/0.50 ![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))),
% 0.21/0.50 inference(skolemize,[status(sab)],[34])).
% 0.21/0.50 tff(36,plain,
% 0.21/0.50 (![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.21/0.50 tff(37,plain,
% 0.21/0.50 (((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | ((~p3(c24, c24)) | (~p3(c24, f4(f7(c17, c18), f14(c18)))) | p3(f4(f7(c17, c18), f14(c18)), c24))) <=> ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | (~p3(c24, c24)) | (~p3(c24, f4(f7(c17, c18), f14(c18)))) | p3(f4(f7(c17, c18), f14(c18)), c24))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(38,plain,
% 0.21/0.50 ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | ((~p3(c24, c24)) | (~p3(c24, f4(f7(c17, c18), f14(c18)))) | p3(f4(f7(c17, c18), f14(c18)), c24))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(39,plain,
% 0.21/0.50 ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | (~p3(c24, c24)) | (~p3(c24, f4(f7(c17, c18), f14(c18)))) | p3(f4(f7(c17, c18), f14(c18)), c24)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.50 tff(40,plain,
% 0.21/0.50 (p3(f4(f7(c17, c18), f14(c18)), c24)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[39, 36, 26, 9])).
% 0.21/0.50 tff(41,assumption,(~p2(f7(c17, c18), f7(c17, c18))), introduced(assumption)).
% 0.21/0.50 tff(42,plain,
% 0.21/0.50 (^[X33: $i] : refl(p2(X33, X33) <=> p2(X33, X33))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(43,plain,
% 0.21/0.50 (![X33: $i] : p2(X33, X33) <=> ![X33: $i] : p2(X33, X33)),
% 0.21/0.50 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.50 tff(44,plain,
% 0.21/0.50 (![X33: $i] : p2(X33, X33) <=> ![X33: $i] : p2(X33, X33)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(45,axiom,(![X33: $i] : p2(X33, X33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_6')).
% 0.21/0.50 tff(46,plain,
% 0.21/0.50 (![X33: $i] : p2(X33, X33)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.50 tff(47,plain,(
% 0.21/0.50 ![X33: $i] : p2(X33, X33)),
% 0.21/0.50 inference(skolemize,[status(sab)],[46])).
% 0.21/0.50 tff(48,plain,
% 0.21/0.50 (![X33: $i] : p2(X33, X33)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.50 tff(49,plain,
% 0.21/0.50 ((~![X33: $i] : p2(X33, X33)) | p2(f7(c17, c18), f7(c17, c18))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(50,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[49, 48, 41])).
% 0.21/0.50 tff(51,plain,(p2(f7(c17, c18), f7(c17, c18))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.50 tff(52,assumption,(~p3(f13(c18), f14(c18))), introduced(assumption)).
% 0.21/0.50 tff(53,plain,
% 0.21/0.50 (^[X31: $i] : refl(((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22)) <=> ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(54,plain,
% 0.21/0.50 (![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22)) <=> ![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.50 tff(55,plain,
% 0.21/0.50 (![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22)) <=> ![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(56,plain,
% 0.21/0.50 (^[X31: $i] : rewrite((p16(c17, c20, f9(c19, X31), f13(X31), c22) | (~p15(X31, c19))) <=> ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(57,plain,
% 0.21/0.50 (![X31: $i] : (p16(c17, c20, f9(c19, X31), f13(X31), c22) | (~p15(X31, c19))) <=> ![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.50 tff(58,axiom,(![X31: $i] : (p16(c17, c20, f9(c19, X31), f13(X31), c22) | (~p15(X31, c19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p16_22')).
% 0.21/0.50 tff(59,plain,
% 0.21/0.50 (![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.50 tff(60,plain,
% 0.21/0.50 (![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.50 tff(61,plain,(
% 0.21/0.50 ![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22))),
% 0.21/0.50 inference(skolemize,[status(sab)],[60])).
% 0.21/0.50 tff(62,plain,
% 0.21/0.50 (![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.21/0.50 tff(63,plain,
% 0.21/0.50 (((~![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22))) | ((~p15(c18, c19)) | p16(c17, c20, f9(c19, c18), f13(c18), c22))) <=> ((~![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22))) | (~p15(c18, c19)) | p16(c17, c20, f9(c19, c18), f13(c18), c22))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(64,plain,
% 0.21/0.50 ((~![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22))) | ((~p15(c18, c19)) | p16(c17, c20, f9(c19, c18), f13(c18), c22))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(65,plain,
% 0.21/0.50 ((~![X31: $i] : ((~p15(X31, c19)) | p16(c17, c20, f9(c19, X31), f13(X31), c22))) | (~p15(c18, c19)) | p16(c17, c20, f9(c19, c18), f13(c18), c22)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.21/0.50 tff(66,plain,
% 0.21/0.50 (p16(c17, c20, f9(c19, c18), f13(c18), c22)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[65, 22, 62])).
% 0.21/0.50 tff(67,plain,
% 0.21/0.50 (^[X32: $i] : refl(((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25)) <=> ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(68,plain,
% 0.21/0.50 (![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25)) <=> ![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[67])).
% 0.21/0.50 tff(69,plain,
% 0.21/0.50 (![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25)) <=> ![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(70,plain,
% 0.21/0.50 (^[X32: $i] : rewrite((p16(c17, c20, f9(c19, X32), f14(X32), c25) | (~p15(X32, c19))) <=> ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(71,plain,
% 0.21/0.50 (![X32: $i] : (p16(c17, c20, f9(c19, X32), f14(X32), c25) | (~p15(X32, c19))) <=> ![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[70])).
% 0.21/0.50 tff(72,axiom,(![X32: $i] : (p16(c17, c20, f9(c19, X32), f14(X32), c25) | (~p15(X32, c19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p16_23')).
% 0.21/0.50 tff(73,plain,
% 0.21/0.50 (![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.50 tff(74,plain,
% 0.21/0.50 (![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.21/0.50 tff(75,plain,(
% 0.21/0.50 ![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25))),
% 0.21/0.50 inference(skolemize,[status(sab)],[74])).
% 0.21/0.50 tff(76,plain,
% 0.21/0.50 (![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.21/0.50 tff(77,plain,
% 0.21/0.50 (((~![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25))) | ((~p15(c18, c19)) | p16(c17, c20, f9(c19, c18), f14(c18), c25))) <=> ((~![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25))) | (~p15(c18, c19)) | p16(c17, c20, f9(c19, c18), f14(c18), c25))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(78,plain,
% 0.21/0.50 ((~![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25))) | ((~p15(c18, c19)) | p16(c17, c20, f9(c19, c18), f14(c18), c25))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(79,plain,
% 0.21/0.50 ((~![X32: $i] : ((~p15(X32, c19)) | p16(c17, c20, f9(c19, X32), f14(X32), c25))) | (~p15(c18, c19)) | p16(c17, c20, f9(c19, c18), f14(c18), c25)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.21/0.50 tff(80,plain,
% 0.21/0.50 (p16(c17, c20, f9(c19, c18), f14(c18), c25)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[79, 22, 76])).
% 0.21/0.50 tff(81,plain,
% 0.21/0.50 (^[X6: $i, X4: $i, X3: $i, X5: $i] : refl(((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6)) <=> ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6)))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(82,plain,
% 0.21/0.50 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6)) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[81])).
% 0.21/0.50 tff(83,plain,
% 0.21/0.50 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6)) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(84,plain,
% 0.21/0.50 (^[X6: $i, X4: $i, X3: $i, X5: $i] : trans(monotonicity(rewrite((p3(X5, X6) | (~p16(c17, c20, X4, X6, X3))) <=> ((~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))), (((p3(X5, X6) | (~p16(c17, c20, X4, X6, X3))) | (~p16(c17, c20, X4, X5, c22))) <=> (((~p16(c17, c20, X4, X6, X3)) | p3(X5, X6)) | (~p16(c17, c20, X4, X5, c22))))), rewrite((((~p16(c17, c20, X4, X6, X3)) | p3(X5, X6)) | (~p16(c17, c20, X4, X5, c22))) <=> ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))), (((p3(X5, X6) | (~p16(c17, c20, X4, X6, X3))) | (~p16(c17, c20, X4, X5, c22))) <=> ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(85,plain,
% 0.21/0.50 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((p3(X5, X6) | (~p16(c17, c20, X4, X6, X3))) | (~p16(c17, c20, X4, X5, c22))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.51 tff(86,axiom,(![X6: $i, X4: $i, X3: $i, X5: $i] : ((p3(X5, X6) | (~p16(c17, c20, X4, X6, X3))) | (~p16(c17, c20, X4, X5, c22)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_28')).
% 0.21/0.51 tff(87,plain,
% 0.21/0.51 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.51 tff(88,plain,
% 0.21/0.51 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.21/0.51 tff(89,plain,(
% 0.21/0.51 ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))),
% 0.21/0.51 inference(skolemize,[status(sab)],[88])).
% 0.21/0.51 tff(90,plain,
% 0.21/0.51 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.21/0.51 tff(91,plain,
% 0.21/0.51 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))) | ((~p16(c17, c20, f9(c19, c18), f13(c18), c22)) | (~p16(c17, c20, f9(c19, c18), f14(c18), c25)) | p3(f13(c18), f14(c18)))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))) | (~p16(c17, c20, f9(c19, c18), f13(c18), c22)) | (~p16(c17, c20, f9(c19, c18), f14(c18), c25)) | p3(f13(c18), f14(c18)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(92,plain,
% 0.21/0.51 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))) | ((~p16(c17, c20, f9(c19, c18), f13(c18), c22)) | (~p16(c17, c20, f9(c19, c18), f14(c18), c25)) | p3(f13(c18), f14(c18)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(93,plain,
% 0.21/0.51 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p16(c17, c20, X4, X5, c22)) | (~p16(c17, c20, X4, X6, X3)) | p3(X5, X6))) | (~p16(c17, c20, f9(c19, c18), f13(c18), c22)) | (~p16(c17, c20, f9(c19, c18), f14(c18), c25)) | p3(f13(c18), f14(c18))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.51 tff(94,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[93, 90, 80, 66, 52])).
% 0.21/0.51 tff(95,plain,(p3(f13(c18), f14(c18))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(96,plain,
% 0.21/0.51 (^[X57: $i, X59: $i, X60: $i, X58: $i] : refl(((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60))) <=> ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(97,plain,
% 0.21/0.51 (![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60))) <=> ![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.51 tff(98,plain,
% 0.21/0.51 (![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60))) <=> ![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(99,plain,
% 0.21/0.51 (^[X57: $i, X59: $i, X60: $i, X58: $i] : trans(monotonicity(rewrite((p3(f4(X57, X58), f4(X59, X60)) | (~p2(X57, X59))) <=> ((~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))), (((p3(f4(X57, X58), f4(X59, X60)) | (~p2(X57, X59))) | (~p3(X58, X60))) <=> (((~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60))) | (~p3(X58, X60))))), rewrite((((~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60))) | (~p3(X58, X60))) <=> ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))), (((p3(f4(X57, X58), f4(X59, X60)) | (~p2(X57, X59))) | (~p3(X58, X60))) <=> ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(100,plain,
% 0.21/0.51 (![X57: $i, X59: $i, X60: $i, X58: $i] : ((p3(f4(X57, X58), f4(X59, X60)) | (~p2(X57, X59))) | (~p3(X58, X60))) <=> ![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[99])).
% 0.21/0.51 tff(101,axiom,(![X57: $i, X59: $i, X60: $i, X58: $i] : ((p3(f4(X57, X58), f4(X59, X60)) | (~p2(X57, X59))) | (~p3(X58, X60)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_27')).
% 0.21/0.51 tff(102,plain,
% 0.21/0.51 (![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.51 tff(103,plain,
% 0.21/0.51 (![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.21/0.51 tff(104,plain,(
% 0.21/0.51 ![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[103])).
% 0.21/0.51 tff(105,plain,
% 0.21/0.51 (![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.21/0.51 tff(106,plain,
% 0.21/0.51 (((~![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))) | ((~p2(f7(c17, c18), f7(c17, c18))) | (~p3(f13(c18), f14(c18))) | p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18))))) <=> ((~![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))) | (~p2(f7(c17, c18), f7(c17, c18))) | (~p3(f13(c18), f14(c18))) | p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(107,plain,
% 0.21/0.51 (((~p3(f13(c18), f14(c18))) | (~p2(f7(c17, c18), f7(c17, c18))) | p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18)))) <=> ((~p2(f7(c17, c18), f7(c17, c18))) | (~p3(f13(c18), f14(c18))) | p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(108,plain,
% 0.21/0.51 (((~![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))) | ((~p3(f13(c18), f14(c18))) | (~p2(f7(c17, c18), f7(c17, c18))) | p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18))))) <=> ((~![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))) | ((~p2(f7(c17, c18), f7(c17, c18))) | (~p3(f13(c18), f14(c18))) | p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18)))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[107])).
% 0.21/0.51 tff(109,plain,
% 0.21/0.51 (((~![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))) | ((~p3(f13(c18), f14(c18))) | (~p2(f7(c17, c18), f7(c17, c18))) | p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18))))) <=> ((~![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))) | (~p2(f7(c17, c18), f7(c17, c18))) | (~p3(f13(c18), f14(c18))) | p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[108, 106])).
% 0.21/0.51 tff(110,plain,
% 0.21/0.51 ((~![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))) | ((~p3(f13(c18), f14(c18))) | (~p2(f7(c17, c18), f7(c17, c18))) | p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(111,plain,
% 0.21/0.51 ((~![X57: $i, X59: $i, X60: $i, X58: $i] : ((~p3(X58, X60)) | (~p2(X57, X59)) | p3(f4(X57, X58), f4(X59, X60)))) | (~p2(f7(c17, c18), f7(c17, c18))) | (~p3(f13(c18), f14(c18))) | p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.51 tff(112,plain,
% 0.21/0.51 ((~p2(f7(c17, c18), f7(c17, c18))) | (~p3(f13(c18), f14(c18))) | p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[111, 105])).
% 0.21/0.51 tff(113,plain,
% 0.21/0.51 ((~p2(f7(c17, c18), f7(c17, c18))) | p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[112, 95])).
% 0.21/0.51 tff(114,plain,
% 0.21/0.51 (p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[113, 51])).
% 0.21/0.51 tff(115,assumption,(~p3(f4(f7(c17, c18), f14(c18)), c23)), introduced(assumption)).
% 0.21/0.51 tff(116,assumption,(~p3(c23, c23)), introduced(assumption)).
% 0.21/0.51 tff(117,plain,
% 0.21/0.51 ((~![X40: $i] : p3(X40, X40)) | p3(c23, c23)),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(118,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[117, 7, 116])).
% 0.21/0.51 tff(119,plain,(p3(c23, c23)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(120,plain,
% 0.21/0.51 (^[X31: $i] : refl(((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31)))) <=> ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(121,plain,
% 0.21/0.51 (![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31)))) <=> ![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.51 tff(122,plain,
% 0.21/0.51 (![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31)))) <=> ![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(123,plain,
% 0.21/0.51 (^[X31: $i] : rewrite((p3(c23, f4(f7(c17, X31), f13(X31))) | (~p15(X31, c19))) <=> ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(124,plain,
% 0.21/0.51 (![X31: $i] : (p3(c23, f4(f7(c17, X31), f13(X31))) | (~p15(X31, c19))) <=> ![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[123])).
% 0.21/0.51 tff(125,axiom,(![X31: $i] : (p3(c23, f4(f7(c17, X31), f13(X31))) | (~p15(X31, c19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_21')).
% 0.21/0.51 tff(126,plain,
% 0.21/0.51 (![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.21/0.51 tff(127,plain,
% 0.21/0.51 (![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.21/0.51 tff(128,plain,(
% 0.21/0.51 ![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[127])).
% 0.21/0.51 tff(129,plain,
% 0.21/0.51 (![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.21/0.51 tff(130,plain,
% 0.21/0.51 (((~![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31))))) | ((~p15(c18, c19)) | p3(c23, f4(f7(c17, c18), f13(c18))))) <=> ((~![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31))))) | (~p15(c18, c19)) | p3(c23, f4(f7(c17, c18), f13(c18))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(131,plain,
% 0.21/0.51 ((~![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31))))) | ((~p15(c18, c19)) | p3(c23, f4(f7(c17, c18), f13(c18))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(132,plain,
% 0.21/0.51 ((~![X31: $i] : ((~p15(X31, c19)) | p3(c23, f4(f7(c17, X31), f13(X31))))) | (~p15(c18, c19)) | p3(c23, f4(f7(c17, c18), f13(c18)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.51 tff(133,plain,
% 0.21/0.51 (p3(c23, f4(f7(c17, c18), f13(c18)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[132, 22, 129])).
% 0.21/0.51 tff(134,plain,
% 0.21/0.51 (((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | ((~p3(c23, c23)) | (~p3(c23, f4(f7(c17, c18), f13(c18)))) | p3(f4(f7(c17, c18), f13(c18)), c23))) <=> ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | (~p3(c23, c23)) | (~p3(c23, f4(f7(c17, c18), f13(c18)))) | p3(f4(f7(c17, c18), f13(c18)), c23))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(135,plain,
% 0.21/0.51 ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | ((~p3(c23, c23)) | (~p3(c23, f4(f7(c17, c18), f13(c18)))) | p3(f4(f7(c17, c18), f13(c18)), c23))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(136,plain,
% 0.21/0.51 ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | (~p3(c23, c23)) | (~p3(c23, f4(f7(c17, c18), f13(c18)))) | p3(f4(f7(c17, c18), f13(c18)), c23)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.51 tff(137,plain,
% 0.21/0.51 (p3(f4(f7(c17, c18), f13(c18)), c23)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[136, 36, 133, 119])).
% 0.21/0.51 tff(138,assumption,(p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18)))), introduced(assumption)).
% 0.21/0.51 tff(139,plain,
% 0.21/0.51 (((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | ((~p3(f4(f7(c17, c18), f13(c18)), c23)) | (~p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18)))) | p3(f4(f7(c17, c18), f14(c18)), c23))) <=> ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | (~p3(f4(f7(c17, c18), f13(c18)), c23)) | (~p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18)))) | p3(f4(f7(c17, c18), f14(c18)), c23))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(140,plain,
% 0.21/0.51 ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | ((~p3(f4(f7(c17, c18), f13(c18)), c23)) | (~p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18)))) | p3(f4(f7(c17, c18), f14(c18)), c23))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(141,plain,
% 0.21/0.51 ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | (~p3(f4(f7(c17, c18), f13(c18)), c23)) | (~p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18)))) | p3(f4(f7(c17, c18), f14(c18)), c23)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.21/0.51 tff(142,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[141, 36, 138, 137, 115])).
% 0.21/0.51 tff(143,plain,((~p3(f4(f7(c17, c18), f13(c18)), f4(f7(c17, c18), f14(c18)))) | p3(f4(f7(c17, c18), f14(c18)), c23)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.51 tff(144,plain,
% 0.21/0.51 (p3(f4(f7(c17, c18), f14(c18)), c23)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[143, 114])).
% 0.21/0.51 tff(145,plain,
% 0.21/0.51 ((~p3(c23, c24)) <=> (~p3(c23, c24))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(146,axiom,(~p3(c23, c24)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p3_8')).
% 0.21/0.51 tff(147,plain,
% 0.21/0.51 (~p3(c23, c24)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.21/0.51 tff(148,plain,
% 0.21/0.51 (((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | (p3(c23, c24) | (~p3(c24, c24)) | (~p3(c24, c23)))) <=> ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | p3(c23, c24) | (~p3(c24, c24)) | (~p3(c24, c23)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(149,plain,
% 0.21/0.51 (((~p3(c24, c24)) | (~p3(c24, c23)) | p3(c23, c24)) <=> (p3(c23, c24) | (~p3(c24, c24)) | (~p3(c24, c23)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(150,plain,
% 0.21/0.51 (((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | ((~p3(c24, c24)) | (~p3(c24, c23)) | p3(c23, c24))) <=> ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | (p3(c23, c24) | (~p3(c24, c24)) | (~p3(c24, c23))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[149])).
% 0.21/0.51 tff(151,plain,
% 0.21/0.51 (((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | ((~p3(c24, c24)) | (~p3(c24, c23)) | p3(c23, c24))) <=> ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | p3(c23, c24) | (~p3(c24, c24)) | (~p3(c24, c23)))),
% 0.21/0.51 inference(transitivity,[status(thm)],[150, 148])).
% 0.21/0.51 tff(152,plain,
% 0.21/0.51 ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | ((~p3(c24, c24)) | (~p3(c24, c23)) | p3(c23, c24))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(153,plain,
% 0.21/0.51 ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | p3(c23, c24) | (~p3(c24, c24)) | (~p3(c24, c23))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.51 tff(154,plain,
% 0.21/0.51 ((~p3(c24, c24)) | (~p3(c24, c23))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[153, 147, 36])).
% 0.21/0.51 tff(155,plain,
% 0.21/0.51 (~p3(c24, c23)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[154, 9])).
% 0.21/0.51 tff(156,plain,
% 0.21/0.51 (((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | ((~p3(f4(f7(c17, c18), f14(c18)), c23)) | (~p3(f4(f7(c17, c18), f14(c18)), c24)) | p3(c24, c23))) <=> ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | (~p3(f4(f7(c17, c18), f14(c18)), c23)) | (~p3(f4(f7(c17, c18), f14(c18)), c24)) | p3(c24, c23))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(157,plain,
% 0.21/0.51 ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | ((~p3(f4(f7(c17, c18), f14(c18)), c23)) | (~p3(f4(f7(c17, c18), f14(c18)), c24)) | p3(c24, c23))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(158,plain,
% 0.21/0.51 ((~![X42: $i, X41: $i, X40: $i] : ((~p3(X40, X42)) | (~p3(X40, X41)) | p3(X41, X42))) | (~p3(f4(f7(c17, c18), f14(c18)), c23)) | (~p3(f4(f7(c17, c18), f14(c18)), c24)) | p3(c24, c23)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.51 tff(159,plain,
% 0.21/0.51 ($false),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[158, 36, 155, 144, 40])).
% 0.21/0.51 % SZS output end Proof
% 0.21/0.52 % E exiting
%------------------------------------------------------------------------------