%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN626-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN626-1 : TPTP v9.0.0. Released v2.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.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 12:38:10 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(p7_type, type, (
% 0.12/0.38 p7: ( $i * $i ) > $o)).
% 0.12/0.38 tff(f12_type, type, (
% 0.12/0.38 f12: $i > $i)).
% 0.12/0.38 tff(f13_type, type, (
% 0.12/0.38 f13: $i > $i)).
% 0.12/0.38 tff(f8_type, type, (
% 0.12/0.38 f8: ( $i * $i ) > $i)).
% 0.12/0.38 tff(f9_type, type, (
% 0.12/0.38 f9: ( $i * $i ) > $i)).
% 0.12/0.38 tff(c24_type, type, (
% 0.12/0.38 c24: $i)).
% 0.12/0.38 tff(c23_type, type, (
% 0.12/0.38 c23: $i)).
% 0.12/0.38 tff(f5_type, type, (
% 0.12/0.38 f5: $i > $i)).
% 0.12/0.38 tff(c20_type, type, (
% 0.12/0.38 c20: $i)).
% 0.12/0.38 tff(p11_type, type, (
% 0.12/0.38 p11: ( $i * $i ) > $o)).
% 0.12/0.38 tff(p16_type, type, (
% 0.12/0.38 p16: ( $i * $i ) > $o)).
% 0.12/0.38 tff(c22_type, type, (
% 0.12/0.38 c22: $i)).
% 0.12/0.38 tff(p15_type, type, (
% 0.12/0.38 p15: ( $i * $i ) > $o)).
% 0.12/0.38 tff(p6_type, type, (
% 0.12/0.38 p6: ( $i * $i ) > $o)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X5: $i] : refl(p11(f13(f12(X5)), X5) <=> p11(f13(f12(X5)), X5))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X5: $i] : p11(f13(f12(X5)), X5) <=> ![X5: $i] : p11(f13(f12(X5)), X5)),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X5: $i] : p11(f13(f12(X5)), X5) <=> ![X5: $i] : p11(f13(f12(X5)), X5)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(![X5: $i] : p11(f13(f12(X5)), X5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_6')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X5: $i] : p11(f13(f12(X5)), X5)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,(
% 0.12/0.38 ![X5: $i] : p11(f13(f12(X5)), X5)),
% 0.12/0.38 inference(skolemize,[status(sab)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![X5: $i] : p11(f13(f12(X5)), X5)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![X5: $i] : p11(f13(f12(X5)), X5)) | p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (^[X0: $i, X2: $i, X1: $i] : refl(((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2)) <=> ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p11(X1, X2) | (~p11(X0, X1))) <=> ((~p11(X0, X1)) | p11(X1, X2))), (((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))) <=> (((~p11(X0, X1)) | p11(X1, X2)) | (~p11(X0, X2))))), rewrite((((~p11(X0, X1)) | p11(X1, X2)) | (~p11(X0, X2))) <=> ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))), (((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))) <=> ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![X0: $i, X2: $i, X1: $i] : ((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.12/0.38 tff(15,axiom,(![X0: $i, X2: $i, X1: $i] : ((p11(X1, X2) | (~p11(X0, X1))) | (~p11(X0, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_16')).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.12/0.38 tff(18,plain,(
% 0.12/0.38 ![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))),
% 0.12/0.38 inference(skolemize,[status(sab)],[17])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))) | ((~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))) | (~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (((~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | (~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24))))) <=> ((~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24)))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))) | ((~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | (~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))) | ((~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24))))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[21])).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))) | ((~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | (~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))) | (~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24)))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[22, 20])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))) | ((~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | (~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24)))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p11(X0, X2)) | (~p11(X0, X1)) | p11(X1, X2))) | (~p11(f13(f12(f13(f8(f5(c20), f9(c23, c24))))), f13(f8(f5(c20), f9(c23, c24))))) | p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[25, 19, 9])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (^[X57: $i, X58: $i] : refl(((~p11(X57, X58)) | p7(f12(X57), f12(X58))) <=> ((~p11(X57, X58)) | p7(f12(X57), f12(X58))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 (![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58))) <=> ![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58))) <=> ![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (^[X57: $i, X58: $i] : rewrite((p7(f12(X57), f12(X58)) | (~p11(X57, X58))) <=> ((~p11(X57, X58)) | p7(f12(X57), f12(X58))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (![X57: $i, X58: $i] : (p7(f12(X57), f12(X58)) | (~p11(X57, X58))) <=> ![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.38 tff(32,axiom,(![X57: $i, X58: $i] : (p7(f12(X57), f12(X58)) | (~p11(X57, X58)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_12')).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.39 tff(35,plain,(
% 0.19/0.39 ![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[34])).
% 0.19/0.39 tff(36,plain,
% 0.19/0.39 (![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.19/0.39 tff(37,plain,
% 0.19/0.39 (((~![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58)))) | ((~p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24))))) | p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24))))))) <=> ((~![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58)))) | (~p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24))))) | p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(38,plain,
% 0.19/0.39 ((~![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58)))) | ((~p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24))))) | p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(39,plain,
% 0.19/0.39 ((~![X57: $i, X58: $i] : ((~p11(X57, X58)) | p7(f12(X57), f12(X58)))) | (~p11(f13(f8(f5(c20), f9(c23, c24))), f13(f8(f5(c20), f9(c23, c24))))) | p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24)))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.19/0.39 tff(40,plain,
% 0.19/0.39 (p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24)))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[39, 36, 26])).
% 0.19/0.39 tff(41,plain,
% 0.19/0.39 (p15(c22, f8(f5(c20), f9(c23, c24))) <=> p15(c22, f8(f5(c20), f9(c23, c24)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(42,axiom,(p15(c22, f8(f5(c20), f9(c23, c24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p15_9')).
% 0.19/0.39 tff(43,plain,
% 0.19/0.39 (p15(c22, f8(f5(c20), f9(c23, c24)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.39 tff(44,plain,
% 0.19/0.39 (^[X14: $i, X15: $i] : refl(((~p15(X14, X15)) | p16(X14, X15)) <=> ((~p15(X14, X15)) | p16(X14, X15)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(45,plain,
% 0.19/0.39 (![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15)) <=> ![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[44])).
% 0.19/0.39 tff(46,plain,
% 0.19/0.39 (![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15)) <=> ![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(47,plain,
% 0.19/0.39 (^[X14: $i, X15: $i] : rewrite((p16(X14, X15) | (~p15(X14, X15))) <=> ((~p15(X14, X15)) | p16(X14, X15)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(48,plain,
% 0.19/0.39 (![X14: $i, X15: $i] : (p16(X14, X15) | (~p15(X14, X15))) <=> ![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.39 tff(49,axiom,(![X14: $i, X15: $i] : (p16(X14, X15) | (~p15(X14, X15)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p16_8')).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.19/0.39 tff(52,plain,(
% 0.19/0.39 ![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15))),
% 0.19/0.39 inference(skolemize,[status(sab)],[51])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.19/0.39 tff(54,plain,
% 0.19/0.39 (((~![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15))) | ((~p15(c22, f8(f5(c20), f9(c23, c24)))) | p16(c22, f8(f5(c20), f9(c23, c24))))) <=> ((~![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15))) | (~p15(c22, f8(f5(c20), f9(c23, c24)))) | p16(c22, f8(f5(c20), f9(c23, c24))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 ((~![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15))) | ((~p15(c22, f8(f5(c20), f9(c23, c24)))) | p16(c22, f8(f5(c20), f9(c23, c24))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 ((~![X14: $i, X15: $i] : ((~p15(X14, X15)) | p16(X14, X15))) | (~p15(c22, f8(f5(c20), f9(c23, c24)))) | p16(c22, f8(f5(c20), f9(c23, c24)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (p16(c22, f8(f5(c20), f9(c23, c24)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[56, 53, 43])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (^[X20: $i] : refl((p7(f12(f13(X20)), X20) | (~p16(c22, X20))) <=> (p7(f12(f13(X20)), X20) | (~p16(c22, X20))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (![X20: $i] : (p7(f12(f13(X20)), X20) | (~p16(c22, X20))) <=> ![X20: $i] : (p7(f12(f13(X20)), X20) | (~p16(c22, X20)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (![X20: $i] : (p7(f12(f13(X20)), X20) | (~p16(c22, X20))) <=> ![X20: $i] : (p7(f12(f13(X20)), X20) | (~p16(c22, X20)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(61,axiom,(![X20: $i] : (p7(f12(f13(X20)), X20) | (~p16(c22, X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_15')).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![X20: $i] : (p7(f12(f13(X20)), X20) | (~p16(c22, X20)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.19/0.39 tff(63,plain,(
% 0.19/0.39 ![X20: $i] : (p7(f12(f13(X20)), X20) | (~p16(c22, X20)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[62])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (![X20: $i] : (p7(f12(f13(X20)), X20) | (~p16(c22, X20)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (((~![X20: $i] : (p7(f12(f13(X20)), X20) | (~p16(c22, X20)))) | (p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24))) | (~p16(c22, f8(f5(c20), f9(c23, c24)))))) <=> ((~![X20: $i] : (p7(f12(f13(X20)), X20) | (~p16(c22, X20)))) | p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24))) | (~p16(c22, f8(f5(c20), f9(c23, c24)))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 ((~![X20: $i] : (p7(f12(f13(X20)), X20) | (~p16(c22, X20)))) | (p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24))) | (~p16(c22, f8(f5(c20), f9(c23, c24)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 ((~![X20: $i] : (p7(f12(f13(X20)), X20) | (~p16(c22, X20)))) | p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24))) | (~p16(c22, f8(f5(c20), f9(c23, c24))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[67, 64, 57])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (^[X56: $i, X55: $i, X54: $i] : refl(((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56)) <=> ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(70,plain,
% 0.19/0.39 (![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56)) <=> ![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[69])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56)) <=> ![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (^[X56: $i, X55: $i, X54: $i] : trans(monotonicity(rewrite((p7(X55, X56) | (~p7(X54, X55))) <=> ((~p7(X54, X55)) | p7(X55, X56))), (((p7(X55, X56) | (~p7(X54, X55))) | (~p7(X54, X56))) <=> (((~p7(X54, X55)) | p7(X55, X56)) | (~p7(X54, X56))))), rewrite((((~p7(X54, X55)) | p7(X55, X56)) | (~p7(X54, X56))) <=> ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))), (((p7(X55, X56) | (~p7(X54, X55))) | (~p7(X54, X56))) <=> ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 (![X56: $i, X55: $i, X54: $i] : ((p7(X55, X56) | (~p7(X54, X55))) | (~p7(X54, X56))) <=> ![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.39 tff(74,axiom,(![X56: $i, X55: $i, X54: $i] : ((p7(X55, X56) | (~p7(X54, X55))) | (~p7(X54, X56)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_17')).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 (![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 (![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.19/0.40 tff(77,plain,(
% 0.19/0.40 ![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))),
% 0.19/0.40 inference(skolemize,[status(sab)],[76])).
% 0.19/0.40 tff(78,plain,
% 0.19/0.40 (![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 (((~![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))) | ((~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24)))))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))) | p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))))) <=> ((~![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24)))))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))) | p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(80,plain,
% 0.19/0.40 (((~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24)))))) | p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24)))))) <=> ((~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24)))))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))) | p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(81,plain,
% 0.19/0.40 (((~![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))) | ((~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24)))))) | p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))))) <=> ((~![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))) | ((~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24)))))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))) | p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24)))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[80])).
% 0.19/0.40 tff(82,plain,
% 0.19/0.40 (((~![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))) | ((~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24)))))) | p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))))) <=> ((~![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24)))))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))) | p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[81, 79])).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ((~![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))) | ((~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24)))))) | p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ((~![X56: $i, X55: $i, X54: $i] : ((~p7(X54, X55)) | (~p7(X54, X56)) | p7(X55, X56))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f12(f13(f8(f5(c20), f9(c23, c24)))))) | (~p7(f12(f13(f8(f5(c20), f9(c23, c24)))), f8(f5(c20), f9(c23, c24)))) | p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.19/0.40 tff(85,plain,
% 0.19/0.40 (p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24)))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[84, 78, 68, 40])).
% 0.19/0.40 tff(86,assumption,(~p6(c22, c22)), introduced(assumption)).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 (^[X47: $i] : refl(p6(X47, X47) <=> p6(X47, X47))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (![X47: $i] : p6(X47, X47) <=> ![X47: $i] : p6(X47, X47)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[87])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.40 (![X47: $i] : p6(X47, X47) <=> ![X47: $i] : p6(X47, X47)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(90,axiom,(![X47: $i] : p6(X47, X47)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p6_3')).
% 0.19/0.40 tff(91,plain,
% 0.19/0.40 (![X47: $i] : p6(X47, X47)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.40 tff(92,plain,(
% 0.19/0.40 ![X47: $i] : p6(X47, X47)),
% 0.19/0.40 inference(skolemize,[status(sab)],[91])).
% 0.19/0.40 tff(93,plain,
% 0.19/0.40 (![X47: $i] : p6(X47, X47)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 ((~![X47: $i] : p6(X47, X47)) | p6(c22, c22)),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[94, 93, 86])).
% 0.19/0.40 tff(96,plain,(p6(c22, c22)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 (^[X12: $i, X11: $i, X13: $i, X10: $i] : refl(((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11)) <=> ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 (![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11)) <=> ![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[97])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11)) <=> ![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (^[X12: $i, X11: $i, X13: $i, X10: $i] : trans(monotonicity(trans(monotonicity(rewrite((p15(X10, X11) | (~p6(X12, X10))) <=> ((~p6(X12, X10)) | p15(X10, X11))), (((p15(X10, X11) | (~p6(X12, X10))) | (~p7(X13, X11))) <=> (((~p6(X12, X10)) | p15(X10, X11)) | (~p7(X13, X11))))), rewrite((((~p6(X12, X10)) | p15(X10, X11)) | (~p7(X13, X11))) <=> ((~p6(X12, X10)) | (~p7(X13, X11)) | p15(X10, X11))), (((p15(X10, X11) | (~p6(X12, X10))) | (~p7(X13, X11))) <=> ((~p6(X12, X10)) | (~p7(X13, X11)) | p15(X10, X11)))), ((((p15(X10, X11) | (~p6(X12, X10))) | (~p7(X13, X11))) | (~p15(X12, X13))) <=> (((~p6(X12, X10)) | (~p7(X13, X11)) | p15(X10, X11)) | (~p15(X12, X13))))), rewrite((((~p6(X12, X10)) | (~p7(X13, X11)) | p15(X10, X11)) | (~p15(X12, X13))) <=> ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))), ((((p15(X10, X11) | (~p6(X12, X10))) | (~p7(X13, X11))) | (~p15(X12, X13))) <=> ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 (![X12: $i, X11: $i, X13: $i, X10: $i] : (((p15(X10, X11) | (~p6(X12, X10))) | (~p7(X13, X11))) | (~p15(X12, X13))) <=> ![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[100])).
% 0.19/0.40 tff(102,axiom,(![X12: $i, X11: $i, X13: $i, X10: $i] : (((p15(X10, X11) | (~p6(X12, X10))) | (~p7(X13, X11))) | (~p15(X12, X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p15_31')).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.19/0.40 tff(105,plain,(
% 0.19/0.40 ![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))),
% 0.19/0.40 inference(skolemize,[status(sab)],[104])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 ((~p15(c22, f12(f13(f8(f5(c20), f9(c23, c24)))))) <=> (~p15(c22, f12(f13(f8(f5(c20), f9(c23, c24))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(108,axiom,(~p15(c22, f12(f13(f8(f5(c20), f9(c23, c24)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p15_24')).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (~p15(c22, f12(f13(f8(f5(c20), f9(c23, c24)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (((~![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))) | ((~p6(c22, c22)) | (~p15(c22, f8(f5(c20), f9(c23, c24)))) | (~p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24)))))) | p15(c22, f12(f13(f8(f5(c20), f9(c23, c24))))))) <=> ((~![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))) | (~p6(c22, c22)) | (~p15(c22, f8(f5(c20), f9(c23, c24)))) | (~p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24)))))) | p15(c22, f12(f13(f8(f5(c20), f9(c23, c24))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 ((~![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))) | ((~p6(c22, c22)) | (~p15(c22, f8(f5(c20), f9(c23, c24)))) | (~p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24)))))) | p15(c22, f12(f13(f8(f5(c20), f9(c23, c24))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 ((~![X12: $i, X11: $i, X13: $i, X10: $i] : ((~p6(X12, X10)) | (~p15(X12, X13)) | (~p7(X13, X11)) | p15(X10, X11))) | (~p6(c22, c22)) | (~p15(c22, f8(f5(c20), f9(c23, c24)))) | (~p7(f8(f5(c20), f9(c23, c24)), f12(f13(f8(f5(c20), f9(c23, c24)))))) | p15(c22, f12(f13(f8(f5(c20), f9(c23, c24)))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[112, 43, 109, 106, 96, 85])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------