%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN707-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:39:52 AM UTC 2025
% Result : Unsatisfiable 235.54s 235.76s
% Output : Proof 235.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN707-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.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 12:40:33 EDT 2025
% 0.18/0.33 % CPUTime :
% 235.54/235.76 % SZS status Unsatisfiable
% 235.54/235.76 % SZS output start Proof
% 235.54/235.76 tff(p39_type, type, (
% 235.54/235.76 p39: ( $i * $i ) > $o)).
% 235.54/235.76 tff(f19_type, type, (
% 235.54/235.76 f19: $i > $i)).
% 235.54/235.76 tff(f11_type, type, (
% 235.54/235.76 f11: $i > $i)).
% 235.54/235.76 tff(f13_type, type, (
% 235.54/235.76 f13: ( $i * $i ) > $i)).
% 235.54/235.76 tff(f14_type, type, (
% 235.54/235.76 f14: ( $i * $i ) > $i)).
% 235.54/235.76 tff(f5_type, type, (
% 235.54/235.76 f5: $i > $i)).
% 235.54/235.76 tff(c44_type, type, (
% 235.54/235.76 c44: $i)).
% 235.54/235.76 tff(f6_type, type, (
% 235.54/235.76 f6: $i > $i)).
% 235.54/235.76 tff(f7_type, type, (
% 235.54/235.76 f7: $i > $i)).
% 235.54/235.76 tff(f15_type, type, (
% 235.54/235.76 f15: $i > $i)).
% 235.54/235.76 tff(c56_type, type, (
% 235.54/235.76 c56: $i)).
% 235.54/235.76 tff(p37_type, type, (
% 235.54/235.76 p37: ( $i * $i ) > $o)).
% 235.54/235.76 tff(p10_type, type, (
% 235.54/235.76 p10: ( $i * $i ) > $o)).
% 235.54/235.76 tff(c48_type, type, (
% 235.54/235.76 c48: $i)).
% 235.54/235.76 tff(p38_type, type, (
% 235.54/235.76 p38: $i > $o)).
% 235.54/235.76 tff(p16_type, type, (
% 235.54/235.76 p16: ( $i * $i ) > $o)).
% 235.54/235.76 tff(p9_type, type, (
% 235.54/235.76 p9: ( $i * $i ) > $o)).
% 235.54/235.76 tff(p2_type, type, (
% 235.54/235.76 p2: ( $i * $i ) > $o)).
% 235.54/235.76 tff(p12_type, type, (
% 235.54/235.76 p12: ( $i * $i ) > $o)).
% 235.54/235.76 tff(f28_type, type, (
% 235.54/235.76 f28: $i > $i)).
% 235.54/235.76 tff(1,assumption,(~p10(c56, c56)), introduced(assumption)).
% 235.54/235.76 tff(2,plain,
% 235.54/235.76 (^[X0: $i] : refl(p10(X0, X0) <=> p10(X0, X0))),
% 235.54/235.76 inference(bind,[status(th)],[])).
% 235.54/235.76 tff(3,plain,
% 235.54/235.76 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 235.54/235.76 inference(quant_intro,[status(thm)],[2])).
% 235.54/235.76 tff(4,plain,
% 235.54/235.76 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 235.54/235.76 inference(rewrite,[status(thm)],[])).
% 235.54/235.76 tff(5,axiom,(![X0: $i] : p10(X0, X0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_3')).
% 235.54/235.76 tff(6,plain,
% 235.54/235.76 (![X0: $i] : p10(X0, X0)),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[5, 4])).
% 235.54/235.76 tff(7,plain,(
% 235.54/235.76 ![X0: $i] : p10(X0, X0)),
% 235.54/235.76 inference(skolemize,[status(sab)],[6])).
% 235.54/235.76 tff(8,plain,
% 235.54/235.76 (![X0: $i] : p10(X0, X0)),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[7, 3])).
% 235.54/235.76 tff(9,plain,
% 235.54/235.76 ((~![X0: $i] : p10(X0, X0)) | p10(c56, c56)),
% 235.54/235.76 inference(quant_inst,[status(thm)],[])).
% 235.54/235.76 tff(10,plain,
% 235.54/235.76 ($false),
% 235.54/235.76 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 235.54/235.76 tff(11,plain,(p10(c56, c56)), inference(lemma,lemma(discharge,[]))).
% 235.54/235.76 tff(12,plain,
% 235.54/235.76 (^[X6: $i, X5: $i] : refl(((~p10(X5, X6)) | p10(f15(X5), f15(X6))) <=> ((~p10(X5, X6)) | p10(f15(X5), f15(X6))))),
% 235.54/235.76 inference(bind,[status(th)],[])).
% 235.54/235.76 tff(13,plain,
% 235.54/235.76 (![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6))) <=> ![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6)))),
% 235.54/235.76 inference(quant_intro,[status(thm)],[12])).
% 235.54/235.76 tff(14,plain,
% 235.54/235.76 (![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6))) <=> ![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6)))),
% 235.54/235.76 inference(rewrite,[status(thm)],[])).
% 235.54/235.76 tff(15,plain,
% 235.54/235.76 (^[X6: $i, X5: $i] : rewrite((p10(f15(X5), f15(X6)) | (~p10(X5, X6))) <=> ((~p10(X5, X6)) | p10(f15(X5), f15(X6))))),
% 235.54/235.76 inference(bind,[status(th)],[])).
% 235.54/235.76 tff(16,plain,
% 235.54/235.76 (![X6: $i, X5: $i] : (p10(f15(X5), f15(X6)) | (~p10(X5, X6))) <=> ![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6)))),
% 235.54/235.76 inference(quant_intro,[status(thm)],[15])).
% 235.54/235.76 tff(17,axiom,(![X6: $i, X5: $i] : (p10(f15(X5), f15(X6)) | (~p10(X5, X6)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_35')).
% 235.54/235.76 tff(18,plain,
% 235.54/235.76 (![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6)))),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[17, 16])).
% 235.54/235.76 tff(19,plain,
% 235.54/235.76 (![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6)))),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[18, 14])).
% 235.54/235.76 tff(20,plain,(
% 235.54/235.76 ![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6)))),
% 235.54/235.76 inference(skolemize,[status(sab)],[19])).
% 235.54/235.76 tff(21,plain,
% 235.54/235.76 (![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6)))),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[20, 13])).
% 235.54/235.76 tff(22,plain,
% 235.54/235.76 (((~![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6)))) | ((~p10(c56, c56)) | p10(f15(c56), f15(c56)))) <=> ((~![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6)))) | (~p10(c56, c56)) | p10(f15(c56), f15(c56)))),
% 235.54/235.76 inference(rewrite,[status(thm)],[])).
% 235.54/235.76 tff(23,plain,
% 235.54/235.76 ((~![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6)))) | ((~p10(c56, c56)) | p10(f15(c56), f15(c56)))),
% 235.54/235.76 inference(quant_inst,[status(thm)],[])).
% 235.54/235.76 tff(24,plain,
% 235.54/235.76 ((~![X6: $i, X5: $i] : ((~p10(X5, X6)) | p10(f15(X5), f15(X6)))) | (~p10(c56, c56)) | p10(f15(c56), f15(c56))),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[23, 22])).
% 235.54/235.76 tff(25,plain,
% 235.54/235.76 ((~p10(c56, c56)) | p10(f15(c56), f15(c56))),
% 235.54/235.76 inference(unit_resolution,[status(thm)],[24, 21])).
% 235.54/235.76 tff(26,plain,
% 235.54/235.76 (p10(f15(c56), f15(c56))),
% 235.54/235.76 inference(unit_resolution,[status(thm)],[25, 11])).
% 235.54/235.76 tff(27,plain,
% 235.54/235.76 (p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))) <=> p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))),
% 235.54/235.76 inference(rewrite,[status(thm)],[])).
% 235.54/235.76 tff(28,axiom,(p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_66')).
% 235.54/235.76 tff(29,plain,
% 235.54/235.76 (p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[28, 27])).
% 235.54/235.76 tff(30,plain,
% 235.54/235.76 (^[X96: $i, X93: $i, X95: $i, X94: $i] : refl(((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94)) <=> ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94)))),
% 235.54/235.76 inference(bind,[status(th)],[])).
% 235.54/235.76 tff(31,plain,
% 235.54/235.76 (![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94)) <=> ![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))),
% 235.54/235.76 inference(quant_intro,[status(thm)],[30])).
% 235.54/235.76 tff(32,plain,
% 235.54/235.76 (![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94)) <=> ![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))),
% 235.54/235.76 inference(rewrite,[status(thm)],[])).
% 235.54/235.76 tff(33,plain,
% 235.54/235.76 (^[X96: $i, X93: $i, X95: $i, X94: $i] : trans(monotonicity(trans(monotonicity(rewrite((p37(X93, X94) | (~p10(X96, X94))) <=> ((~p10(X96, X94)) | p37(X93, X94))), (((p37(X93, X94) | (~p10(X96, X94))) | (~p37(X95, X96))) <=> (((~p10(X96, X94)) | p37(X93, X94)) | (~p37(X95, X96))))), rewrite((((~p10(X96, X94)) | p37(X93, X94)) | (~p37(X95, X96))) <=> ((~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))), (((p37(X93, X94) | (~p10(X96, X94))) | (~p37(X95, X96))) <=> ((~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94)))), ((((p37(X93, X94) | (~p10(X96, X94))) | (~p37(X95, X96))) | (~p10(X95, X93))) <=> (((~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94)) | (~p10(X95, X93))))), rewrite((((~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94)) | (~p10(X95, X93))) <=> ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))), ((((p37(X93, X94) | (~p10(X96, X94))) | (~p37(X95, X96))) | (~p10(X95, X93))) <=> ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))))),
% 235.54/235.76 inference(bind,[status(th)],[])).
% 235.54/235.76 tff(34,plain,
% 235.54/235.76 (![X96: $i, X93: $i, X95: $i, X94: $i] : (((p37(X93, X94) | (~p10(X96, X94))) | (~p37(X95, X96))) | (~p10(X95, X93))) <=> ![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))),
% 235.54/235.76 inference(quant_intro,[status(thm)],[33])).
% 235.54/235.76 tff(35,axiom,(![X96: $i, X93: $i, X95: $i, X94: $i] : (((p37(X93, X94) | (~p10(X96, X94))) | (~p37(X95, X96))) | (~p10(X95, X93)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p37_51')).
% 235.54/235.76 tff(36,plain,
% 235.54/235.76 (![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[35, 34])).
% 235.54/235.76 tff(37,plain,
% 235.54/235.76 (![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[36, 32])).
% 235.54/235.76 tff(38,plain,(
% 235.54/235.76 ![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))),
% 235.54/235.76 inference(skolemize,[status(sab)],[37])).
% 235.54/235.76 tff(39,plain,
% 235.54/235.76 (![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[38, 31])).
% 235.54/235.76 tff(40,plain,
% 235.54/235.76 (p37(f15(c56), c48) <=> p37(f15(c56), c48)),
% 235.54/235.76 inference(rewrite,[status(thm)],[])).
% 235.54/235.76 tff(41,axiom,(p37(f15(c56), c48)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p37_13')).
% 235.54/235.76 tff(42,plain,
% 235.54/235.76 (p37(f15(c56), c48)),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[41, 40])).
% 235.54/235.76 tff(43,plain,
% 235.54/235.76 (((~![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))) | ((~p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), c48)) | (~p10(f15(c56), f15(c56))) | p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) <=> ((~![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))) | (~p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), c48)) | (~p10(f15(c56), f15(c56))) | p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))),
% 235.54/235.76 inference(rewrite,[status(thm)],[])).
% 235.54/235.76 tff(44,plain,
% 235.54/235.76 (((~p10(f15(c56), f15(c56))) | (~p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), c48)) | p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) <=> ((~p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), c48)) | (~p10(f15(c56), f15(c56))) | p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))),
% 235.54/235.76 inference(rewrite,[status(thm)],[])).
% 235.54/235.76 tff(45,plain,
% 235.54/235.76 (((~![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))) | ((~p10(f15(c56), f15(c56))) | (~p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), c48)) | p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) <=> ((~![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))) | ((~p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), c48)) | (~p10(f15(c56), f15(c56))) | p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))),
% 235.54/235.76 inference(monotonicity,[status(thm)],[44])).
% 235.54/235.76 tff(46,plain,
% 235.54/235.76 (((~![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))) | ((~p10(f15(c56), f15(c56))) | (~p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), c48)) | p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) <=> ((~![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))) | (~p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), c48)) | (~p10(f15(c56), f15(c56))) | p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))),
% 235.54/235.76 inference(transitivity,[status(thm)],[45, 43])).
% 235.54/235.76 tff(47,plain,
% 235.54/235.76 ((~![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))) | ((~p10(f15(c56), f15(c56))) | (~p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), c48)) | p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))),
% 235.54/235.76 inference(quant_inst,[status(thm)],[])).
% 235.54/235.76 tff(48,plain,
% 235.54/235.76 ((~![X96: $i, X93: $i, X95: $i, X94: $i] : ((~p10(X95, X93)) | (~p10(X96, X94)) | (~p37(X95, X96)) | p37(X93, X94))) | (~p10(c48, f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), c48)) | (~p10(f15(c56), f15(c56))) | p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[47, 46])).
% 235.54/235.76 tff(49,plain,
% 235.54/235.76 (p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))),
% 235.54/235.76 inference(unit_resolution,[status(thm)],[48, 42, 39, 29, 26])).
% 235.54/235.76 tff(50,plain,
% 235.54/235.76 (^[X27: $i] : refl(((~p38(X27)) | p38(f15(X27))) <=> ((~p38(X27)) | p38(f15(X27))))),
% 235.54/235.76 inference(bind,[status(th)],[])).
% 235.54/235.76 tff(51,plain,
% 235.54/235.76 (![X27: $i] : ((~p38(X27)) | p38(f15(X27))) <=> ![X27: $i] : ((~p38(X27)) | p38(f15(X27)))),
% 235.54/235.76 inference(quant_intro,[status(thm)],[50])).
% 235.54/235.76 tff(52,plain,
% 235.54/235.76 (![X27: $i] : ((~p38(X27)) | p38(f15(X27))) <=> ![X27: $i] : ((~p38(X27)) | p38(f15(X27)))),
% 235.54/235.76 inference(rewrite,[status(thm)],[])).
% 235.54/235.76 tff(53,plain,
% 235.54/235.76 (^[X27: $i] : rewrite((p38(f15(X27)) | (~p38(X27))) <=> ((~p38(X27)) | p38(f15(X27))))),
% 235.54/235.76 inference(bind,[status(th)],[])).
% 235.54/235.76 tff(54,plain,
% 235.54/235.76 (![X27: $i] : (p38(f15(X27)) | (~p38(X27))) <=> ![X27: $i] : ((~p38(X27)) | p38(f15(X27)))),
% 235.54/235.76 inference(quant_intro,[status(thm)],[53])).
% 235.54/235.76 tff(55,axiom,(![X27: $i] : (p38(f15(X27)) | (~p38(X27)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p38_15')).
% 235.54/235.76 tff(56,plain,
% 235.54/235.76 (![X27: $i] : ((~p38(X27)) | p38(f15(X27)))),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[55, 54])).
% 235.54/235.76 tff(57,plain,
% 235.54/235.76 (![X27: $i] : ((~p38(X27)) | p38(f15(X27)))),
% 235.54/235.76 inference(modus_ponens,[status(thm)],[56, 52])).
% 235.54/235.77 tff(58,plain,(
% 235.54/235.77 ![X27: $i] : ((~p38(X27)) | p38(f15(X27)))),
% 235.54/235.77 inference(skolemize,[status(sab)],[57])).
% 235.54/235.77 tff(59,plain,
% 235.54/235.77 (![X27: $i] : ((~p38(X27)) | p38(f15(X27)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[58, 51])).
% 235.54/235.77 tff(60,plain,
% 235.54/235.77 (p38(c56) <=> p38(c56)),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(61,axiom,(p38(c56)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','c56_is_p38_1')).
% 235.54/235.77 tff(62,plain,
% 235.54/235.77 (p38(c56)),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[61, 60])).
% 235.54/235.77 tff(63,plain,
% 235.54/235.77 (((~![X27: $i] : ((~p38(X27)) | p38(f15(X27)))) | ((~p38(c56)) | p38(f15(c56)))) <=> ((~![X27: $i] : ((~p38(X27)) | p38(f15(X27)))) | (~p38(c56)) | p38(f15(c56)))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(64,plain,
% 235.54/235.77 ((~![X27: $i] : ((~p38(X27)) | p38(f15(X27)))) | ((~p38(c56)) | p38(f15(c56)))),
% 235.54/235.77 inference(quant_inst,[status(thm)],[])).
% 235.54/235.77 tff(65,plain,
% 235.54/235.77 ((~![X27: $i] : ((~p38(X27)) | p38(f15(X27)))) | (~p38(c56)) | p38(f15(c56))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[64, 63])).
% 235.54/235.77 tff(66,plain,
% 235.54/235.77 (p38(f15(c56))),
% 235.54/235.77 inference(unit_resolution,[status(thm)],[65, 62, 59])).
% 235.54/235.77 tff(67,plain,
% 235.54/235.77 (p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))) <=> p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(68,axiom,(p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','f11_is_p38_64')).
% 235.54/235.77 tff(69,plain,
% 235.54/235.77 (p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[68, 67])).
% 235.54/235.77 tff(70,plain,
% 235.54/235.77 (^[X91: $i, X92: $i] : refl(((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92))) <=> ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92))))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(71,plain,
% 235.54/235.77 (![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92))) <=> ![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))),
% 235.54/235.77 inference(quant_intro,[status(thm)],[70])).
% 235.54/235.77 tff(72,plain,
% 235.54/235.77 (![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92))) <=> ![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(73,plain,
% 235.54/235.77 (^[X91: $i, X92: $i] : trans(monotonicity(trans(monotonicity(rewrite((p39(f19(X91), f19(X92)) | (~p38(X92))) <=> ((~p38(X92)) | p39(f19(X91), f19(X92)))), (((p39(f19(X91), f19(X92)) | (~p38(X92))) | (~p38(X91))) <=> (((~p38(X92)) | p39(f19(X91), f19(X92))) | (~p38(X91))))), rewrite((((~p38(X92)) | p39(f19(X91), f19(X92))) | (~p38(X91))) <=> ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)))), (((p39(f19(X91), f19(X92)) | (~p38(X92))) | (~p38(X91))) <=> ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91))))), ((((p39(f19(X91), f19(X92)) | (~p38(X92))) | (~p38(X91))) | (~p37(X91, X92))) <=> (((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91))) | (~p37(X91, X92))))), rewrite((((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91))) | (~p37(X91, X92))) <=> ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))), ((((p39(f19(X91), f19(X92)) | (~p38(X92))) | (~p38(X91))) | (~p37(X91, X92))) <=> ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(74,plain,
% 235.54/235.77 (![X91: $i, X92: $i] : (((p39(f19(X91), f19(X92)) | (~p38(X92))) | (~p38(X91))) | (~p37(X91, X92))) <=> ![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))),
% 235.54/235.77 inference(quant_intro,[status(thm)],[73])).
% 235.54/235.77 tff(75,axiom,(![X91: $i, X92: $i] : (((p39(f19(X91), f19(X92)) | (~p38(X92))) | (~p38(X91))) | (~p37(X91, X92)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p39_54')).
% 235.54/235.77 tff(76,plain,
% 235.54/235.77 (![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[75, 74])).
% 235.54/235.77 tff(77,plain,
% 235.54/235.77 (![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[76, 72])).
% 235.54/235.77 tff(78,plain,(
% 235.54/235.77 ![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))),
% 235.54/235.77 inference(skolemize,[status(sab)],[77])).
% 235.54/235.77 tff(79,plain,
% 235.54/235.77 (![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[78, 71])).
% 235.54/235.77 tff(80,plain,
% 235.54/235.77 (((~![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))) | ((~p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p38(f15(c56))) | p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))) <=> ((~![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))) | (~p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p38(f15(c56))) | p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(81,plain,
% 235.54/235.77 (((~p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p38(f15(c56))) | (~p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) <=> ((~p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p38(f15(c56))) | p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(82,plain,
% 235.54/235.77 (((~![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))) | ((~p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p38(f15(c56))) | (~p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))) <=> ((~![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))) | ((~p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p38(f15(c56))) | p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))))),
% 235.54/235.77 inference(monotonicity,[status(thm)],[81])).
% 235.54/235.77 tff(83,plain,
% 235.54/235.77 (((~![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))) | ((~p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p38(f15(c56))) | (~p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))) <=> ((~![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))) | (~p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p38(f15(c56))) | p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))),
% 235.54/235.77 inference(transitivity,[status(thm)],[82, 80])).
% 235.54/235.77 tff(84,plain,
% 235.54/235.77 ((~![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))) | ((~p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p38(f15(c56))) | (~p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))),
% 235.54/235.77 inference(quant_inst,[status(thm)],[])).
% 235.54/235.77 tff(85,plain,
% 235.54/235.77 ((~![X91: $i, X92: $i] : ((~p38(X92)) | p39(f19(X91), f19(X92)) | (~p38(X91)) | (~p37(X91, X92)))) | (~p38(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p38(f15(c56))) | p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p37(f15(c56), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[84, 83])).
% 235.54/235.77 tff(86,plain,
% 235.54/235.77 (p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))),
% 235.54/235.77 inference(unit_resolution,[status(thm)],[85, 79, 69, 66, 49])).
% 235.54/235.77 tff(87,assumption,(~p2(f5(c44), f5(c44))), introduced(assumption)).
% 235.54/235.77 tff(88,plain,
% 235.54/235.77 (^[X52: $i] : refl(p2(X52, X52) <=> p2(X52, X52))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(89,plain,
% 235.54/235.77 (![X52: $i] : p2(X52, X52) <=> ![X52: $i] : p2(X52, X52)),
% 235.54/235.77 inference(quant_intro,[status(thm)],[88])).
% 235.54/235.77 tff(90,plain,
% 235.54/235.77 (![X52: $i] : p2(X52, X52) <=> ![X52: $i] : p2(X52, X52)),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(91,axiom,(![X52: $i] : p2(X52, X52)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_7')).
% 235.54/235.77 tff(92,plain,
% 235.54/235.77 (![X52: $i] : p2(X52, X52)),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[91, 90])).
% 235.54/235.77 tff(93,plain,(
% 235.54/235.77 ![X52: $i] : p2(X52, X52)),
% 235.54/235.77 inference(skolemize,[status(sab)],[92])).
% 235.54/235.77 tff(94,plain,
% 235.54/235.77 (![X52: $i] : p2(X52, X52)),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[93, 89])).
% 235.54/235.77 tff(95,plain,
% 235.54/235.77 ((~![X52: $i] : p2(X52, X52)) | p2(f5(c44), f5(c44))),
% 235.54/235.77 inference(quant_inst,[status(thm)],[])).
% 235.54/235.77 tff(96,plain,
% 235.54/235.77 ($false),
% 235.54/235.77 inference(unit_resolution,[status(thm)],[95, 94, 87])).
% 235.54/235.77 tff(97,plain,(p2(f5(c44), f5(c44))), inference(lemma,lemma(discharge,[]))).
% 235.54/235.77 tff(98,assumption,(~p12(f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), introduced(assumption)).
% 235.54/235.77 tff(99,plain,
% 235.54/235.77 (^[X11: $i] : refl(p12(X11, X11) <=> p12(X11, X11))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(100,plain,
% 235.54/235.77 (![X11: $i] : p12(X11, X11) <=> ![X11: $i] : p12(X11, X11)),
% 235.54/235.77 inference(quant_intro,[status(thm)],[99])).
% 235.54/235.77 tff(101,plain,
% 235.54/235.77 (![X11: $i] : p12(X11, X11) <=> ![X11: $i] : p12(X11, X11)),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(102,axiom,(![X11: $i] : p12(X11, X11)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_9')).
% 235.54/235.77 tff(103,plain,
% 235.54/235.77 (![X11: $i] : p12(X11, X11)),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[102, 101])).
% 235.54/235.77 tff(104,plain,(
% 235.54/235.77 ![X11: $i] : p12(X11, X11)),
% 235.54/235.77 inference(skolemize,[status(sab)],[103])).
% 235.54/235.77 tff(105,plain,
% 235.54/235.77 (![X11: $i] : p12(X11, X11)),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[104, 100])).
% 235.54/235.77 tff(106,plain,
% 235.54/235.77 ((~![X11: $i] : p12(X11, X11)) | p12(f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))),
% 235.54/235.77 inference(quant_inst,[status(thm)],[])).
% 235.54/235.77 tff(107,plain,
% 235.54/235.77 ($false),
% 235.54/235.77 inference(unit_resolution,[status(thm)],[106, 105, 98])).
% 235.54/235.77 tff(108,plain,(p12(f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), inference(lemma,lemma(discharge,[]))).
% 235.54/235.77 tff(109,plain,
% 235.54/235.77 (^[X118: $i, X119: $i, X116: $i, X117: $i] : refl(((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119))) <=> ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119))))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(110,plain,
% 235.54/235.77 (![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119))) <=> ![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))),
% 235.54/235.77 inference(quant_intro,[status(thm)],[109])).
% 235.54/235.77 tff(111,plain,
% 235.54/235.77 (![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119))) <=> ![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(112,plain,
% 235.54/235.77 (^[X118: $i, X119: $i, X116: $i, X117: $i] : trans(monotonicity(rewrite((p9(f13(X116, X117), f13(X118, X119)) | (~p12(X117, X119))) <=> ((~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))), (((p9(f13(X116, X117), f13(X118, X119)) | (~p12(X117, X119))) | (~p2(X116, X118))) <=> (((~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119))) | (~p2(X116, X118))))), rewrite((((~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119))) | (~p2(X116, X118))) <=> ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))), (((p9(f13(X116, X117), f13(X118, X119)) | (~p12(X117, X119))) | (~p2(X116, X118))) <=> ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(113,plain,
% 235.54/235.77 (![X118: $i, X119: $i, X116: $i, X117: $i] : ((p9(f13(X116, X117), f13(X118, X119)) | (~p12(X117, X119))) | (~p2(X116, X118))) <=> ![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))),
% 235.54/235.77 inference(quant_intro,[status(thm)],[112])).
% 235.54/235.77 tff(114,axiom,(![X118: $i, X119: $i, X116: $i, X117: $i] : ((p9(f13(X116, X117), f13(X118, X119)) | (~p12(X117, X119))) | (~p2(X116, X118)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p9_55')).
% 235.54/235.77 tff(115,plain,
% 235.54/235.77 (![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[114, 113])).
% 235.54/235.77 tff(116,plain,
% 235.54/235.77 (![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[115, 111])).
% 235.54/235.77 tff(117,plain,(
% 235.54/235.77 ![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))),
% 235.54/235.77 inference(skolemize,[status(sab)],[116])).
% 235.54/235.77 tff(118,plain,
% 235.54/235.77 (![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[117, 110])).
% 235.54/235.77 tff(119,plain,
% 235.54/235.77 (((~![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))) | ((~p2(f5(c44), f5(c44))) | (~p12(f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))) | p9(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))), f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) <=> ((~![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))) | (~p2(f5(c44), f5(c44))) | (~p12(f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))) | p9(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))), f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(120,plain,
% 235.54/235.77 ((~![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))) | ((~p2(f5(c44), f5(c44))) | (~p12(f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))) | p9(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))), f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))),
% 235.54/235.77 inference(quant_inst,[status(thm)],[])).
% 235.54/235.77 tff(121,plain,
% 235.54/235.77 ((~![X118: $i, X119: $i, X116: $i, X117: $i] : ((~p2(X116, X118)) | (~p12(X117, X119)) | p9(f13(X116, X117), f13(X118, X119)))) | (~p2(f5(c44), f5(c44))) | (~p12(f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))) | p9(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))), f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[120, 119])).
% 235.54/235.77 tff(122,plain,
% 235.54/235.77 ((~p2(f5(c44), f5(c44))) | (~p12(f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))) | p9(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))), f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))),
% 235.54/235.77 inference(unit_resolution,[status(thm)],[121, 118])).
% 235.54/235.77 tff(123,plain,
% 235.54/235.77 (p9(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))), f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))),
% 235.54/235.77 inference(unit_resolution,[status(thm)],[122, 108, 97])).
% 235.54/235.77 tff(124,plain,
% 235.54/235.77 (^[X4: $i, X3: $i] : refl(((~p9(X3, X4)) | p10(f11(X3), f11(X4))) <=> ((~p9(X3, X4)) | p10(f11(X3), f11(X4))))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(125,plain,
% 235.54/235.77 (![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4))) <=> ![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 235.54/235.77 inference(quant_intro,[status(thm)],[124])).
% 235.54/235.77 tff(126,plain,
% 235.54/235.77 (![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4))) <=> ![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(127,plain,
% 235.54/235.77 (^[X4: $i, X3: $i] : rewrite((p10(f11(X3), f11(X4)) | (~p9(X3, X4))) <=> ((~p9(X3, X4)) | p10(f11(X3), f11(X4))))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(128,plain,
% 235.54/235.77 (![X4: $i, X3: $i] : (p10(f11(X3), f11(X4)) | (~p9(X3, X4))) <=> ![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 235.54/235.77 inference(quant_intro,[status(thm)],[127])).
% 235.54/235.77 tff(129,axiom,(![X4: $i, X3: $i] : (p10(f11(X3), f11(X4)) | (~p9(X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_20')).
% 235.54/235.77 tff(130,plain,
% 235.54/235.77 (![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[129, 128])).
% 235.54/235.77 tff(131,plain,
% 235.54/235.77 (![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[130, 126])).
% 235.54/235.77 tff(132,plain,(
% 235.54/235.77 ![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 235.54/235.77 inference(skolemize,[status(sab)],[131])).
% 235.54/235.77 tff(133,plain,
% 235.54/235.77 (![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[132, 125])).
% 235.54/235.77 tff(134,plain,
% 235.54/235.77 (((~![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))) | ((~p9(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))), f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))) | p10(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) <=> ((~![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))) | (~p9(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))), f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))) | p10(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(135,plain,
% 235.54/235.77 ((~![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))) | ((~p9(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))), f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))) | p10(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))),
% 235.54/235.77 inference(quant_inst,[status(thm)],[])).
% 235.54/235.77 tff(136,plain,
% 235.54/235.77 ((~![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))) | (~p9(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))), f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))) | p10(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[135, 134])).
% 235.54/235.77 tff(137,plain,
% 235.54/235.77 (p10(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))),
% 235.54/235.77 inference(unit_resolution,[status(thm)],[136, 133, 123])).
% 235.54/235.77 tff(138,plain,
% 235.54/235.77 (^[X25: $i, X26: $i] : refl(((~p10(X25, X26)) | p16(f19(X25), f19(X26))) <=> ((~p10(X25, X26)) | p16(f19(X25), f19(X26))))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(139,plain,
% 235.54/235.77 (![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26))) <=> ![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26)))),
% 235.54/235.77 inference(quant_intro,[status(thm)],[138])).
% 235.54/235.77 tff(140,plain,
% 235.54/235.77 (![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26))) <=> ![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26)))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(141,plain,
% 235.54/235.77 (^[X25: $i, X26: $i] : rewrite((p16(f19(X25), f19(X26)) | (~p10(X25, X26))) <=> ((~p10(X25, X26)) | p16(f19(X25), f19(X26))))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(142,plain,
% 235.54/235.77 (![X25: $i, X26: $i] : (p16(f19(X25), f19(X26)) | (~p10(X25, X26))) <=> ![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26)))),
% 235.54/235.77 inference(quant_intro,[status(thm)],[141])).
% 235.54/235.77 tff(143,axiom,(![X25: $i, X26: $i] : (p16(f19(X25), f19(X26)) | (~p10(X25, X26)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p16_32')).
% 235.54/235.77 tff(144,plain,
% 235.54/235.77 (![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[143, 142])).
% 235.54/235.77 tff(145,plain,
% 235.54/235.77 (![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[144, 140])).
% 235.54/235.77 tff(146,plain,(
% 235.54/235.77 ![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26)))),
% 235.54/235.77 inference(skolemize,[status(sab)],[145])).
% 235.54/235.77 tff(147,plain,
% 235.54/235.77 (![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[146, 139])).
% 235.54/235.77 tff(148,plain,
% 235.54/235.77 (((~![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26)))) | ((~p10(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))) <=> ((~![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26)))) | (~p10(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(149,plain,
% 235.54/235.77 ((~![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26)))) | ((~p10(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))),
% 235.54/235.77 inference(quant_inst,[status(thm)],[])).
% 235.54/235.77 tff(150,plain,
% 235.54/235.77 ((~![X25: $i, X26: $i] : ((~p10(X25, X26)) | p16(f19(X25), f19(X26)))) | (~p10(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))), f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[149, 148])).
% 235.54/235.77 tff(151,plain,
% 235.54/235.77 (p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))),
% 235.54/235.77 inference(unit_resolution,[status(thm)],[150, 147, 137])).
% 235.54/235.77 tff(152,plain,
% 235.54/235.77 (^[X27: $i] : refl(((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27)))) <=> ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27)))))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(153,plain,
% 235.54/235.77 (![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27)))) <=> ![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27))))),
% 235.54/235.77 inference(quant_intro,[status(thm)],[152])).
% 235.54/235.77 tff(154,plain,
% 235.54/235.77 (![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27)))) <=> ![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27))))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(155,plain,
% 235.54/235.77 (^[X27: $i] : rewrite((p16(f19(f15(X27)), f28(f19(X27))) | (~p38(X27))) <=> ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27)))))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(156,plain,
% 235.54/235.77 (![X27: $i] : (p16(f19(f15(X27)), f28(f19(X27))) | (~p38(X27))) <=> ![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27))))),
% 235.54/235.77 inference(quant_intro,[status(thm)],[155])).
% 235.54/235.77 tff(157,axiom,(![X27: $i] : (p16(f19(f15(X27)), f28(f19(X27))) | (~p38(X27)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p16_36')).
% 235.54/235.77 tff(158,plain,
% 235.54/235.77 (![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27))))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[157, 156])).
% 235.54/235.77 tff(159,plain,
% 235.54/235.77 (![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27))))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[158, 154])).
% 235.54/235.77 tff(160,plain,(
% 235.54/235.77 ![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27))))),
% 235.54/235.77 inference(skolemize,[status(sab)],[159])).
% 235.54/235.77 tff(161,plain,
% 235.54/235.77 (![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27))))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[160, 153])).
% 235.54/235.77 tff(162,plain,
% 235.54/235.77 (((~![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27))))) | ((~p38(c56)) | p16(f19(f15(c56)), f28(f19(c56))))) <=> ((~![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27))))) | (~p38(c56)) | p16(f19(f15(c56)), f28(f19(c56))))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(163,plain,
% 235.54/235.77 ((~![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27))))) | ((~p38(c56)) | p16(f19(f15(c56)), f28(f19(c56))))),
% 235.54/235.77 inference(quant_inst,[status(thm)],[])).
% 235.54/235.77 tff(164,plain,
% 235.54/235.77 ((~![X27: $i] : ((~p38(X27)) | p16(f19(f15(X27)), f28(f19(X27))))) | (~p38(c56)) | p16(f19(f15(c56)), f28(f19(c56)))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[163, 162])).
% 235.54/235.77 tff(165,plain,
% 235.54/235.77 (p16(f19(f15(c56)), f28(f19(c56)))),
% 235.54/235.77 inference(unit_resolution,[status(thm)],[164, 62, 161])).
% 235.54/235.77 tff(166,plain,
% 235.54/235.77 ((~p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) <=> (~p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(167,axiom,(~p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p39_69')).
% 235.54/235.77 tff(168,plain,
% 235.54/235.77 (~p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[167, 166])).
% 235.54/235.77 tff(169,plain,
% 235.54/235.77 (^[X99: $i, X100: $i, X101: $i, X102: $i] : refl(((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100)) <=> ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100)))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(170,plain,
% 235.54/235.77 (![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100)) <=> ![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))),
% 235.54/235.77 inference(quant_intro,[status(thm)],[169])).
% 235.54/235.77 tff(171,plain,
% 235.54/235.77 (![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100)) <=> ![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(172,plain,
% 235.54/235.77 (^[X99: $i, X100: $i, X101: $i, X102: $i] : trans(monotonicity(trans(monotonicity(rewrite((p39(X99, X100) | (~p16(X102, X100))) <=> ((~p16(X102, X100)) | p39(X99, X100))), (((p39(X99, X100) | (~p16(X102, X100))) | (~p39(X101, X102))) <=> (((~p16(X102, X100)) | p39(X99, X100)) | (~p39(X101, X102))))), rewrite((((~p16(X102, X100)) | p39(X99, X100)) | (~p39(X101, X102))) <=> ((~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))), (((p39(X99, X100) | (~p16(X102, X100))) | (~p39(X101, X102))) <=> ((~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100)))), ((((p39(X99, X100) | (~p16(X102, X100))) | (~p39(X101, X102))) | (~p16(X101, X99))) <=> (((~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100)) | (~p16(X101, X99))))), rewrite((((~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100)) | (~p16(X101, X99))) <=> ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))), ((((p39(X99, X100) | (~p16(X102, X100))) | (~p39(X101, X102))) | (~p16(X101, X99))) <=> ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))))),
% 235.54/235.77 inference(bind,[status(th)],[])).
% 235.54/235.77 tff(173,plain,
% 235.54/235.77 (![X99: $i, X100: $i, X101: $i, X102: $i] : (((p39(X99, X100) | (~p16(X102, X100))) | (~p39(X101, X102))) | (~p16(X101, X99))) <=> ![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))),
% 235.54/235.77 inference(quant_intro,[status(thm)],[172])).
% 235.54/235.77 tff(174,axiom,(![X99: $i, X100: $i, X101: $i, X102: $i] : (((p39(X99, X100) | (~p16(X102, X100))) | (~p39(X101, X102))) | (~p16(X101, X99)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p39_52')).
% 235.54/235.77 tff(175,plain,
% 235.54/235.77 (![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[174, 173])).
% 235.54/235.77 tff(176,plain,
% 235.54/235.77 (![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[175, 171])).
% 235.54/235.77 tff(177,plain,(
% 235.54/235.77 ![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))),
% 235.54/235.77 inference(skolemize,[status(sab)],[176])).
% 235.54/235.77 tff(178,plain,
% 235.54/235.77 (![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))),
% 235.54/235.77 inference(modus_ponens,[status(thm)],[177, 170])).
% 235.54/235.77 tff(179,plain,
% 235.54/235.77 (((~![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))) | (p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | (~p16(f19(f15(c56)), f28(f19(c56)))) | (~p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))))) <=> ((~![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))) | p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | (~p16(f19(f15(c56)), f28(f19(c56)))) | (~p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))))),
% 235.54/235.77 inference(rewrite,[status(thm)],[])).
% 235.54/235.77 tff(180,plain,
% 235.54/235.77 (((~p16(f19(f15(c56)), f28(f19(c56)))) | (~p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | (~p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) <=> (p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | (~p16(f19(f15(c56)), f28(f19(c56)))) | (~p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))))),
% 235.61/235.87 inference(rewrite,[status(thm)],[])).
% 235.61/235.87 tff(181,plain,
% 235.61/235.87 (((~![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))) | ((~p16(f19(f15(c56)), f28(f19(c56)))) | (~p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | (~p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))) <=> ((~![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))) | (p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | (~p16(f19(f15(c56)), f28(f19(c56)))) | (~p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))))),
% 235.61/235.87 inference(monotonicity,[status(thm)],[180])).
% 235.61/235.87 tff(182,plain,
% 235.61/235.87 (((~![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))) | ((~p16(f19(f15(c56)), f28(f19(c56)))) | (~p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | (~p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))) <=> ((~![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))) | p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | (~p16(f19(f15(c56)), f28(f19(c56)))) | (~p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))))),
% 235.61/235.87 inference(transitivity,[status(thm)],[181, 179])).
% 235.61/235.87 tff(183,plain,
% 235.61/235.87 ((~![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))) | ((~p16(f19(f15(c56)), f28(f19(c56)))) | (~p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | (~p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))),
% 235.61/235.87 inference(quant_inst,[status(thm)],[])).
% 235.61/235.87 tff(184,plain,
% 235.61/235.87 ((~![X99: $i, X100: $i, X101: $i, X102: $i] : ((~p16(X101, X99)) | (~p39(X101, X102)) | (~p16(X102, X100)) | p39(X99, X100))) | p39(f28(f19(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))) | (~p16(f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44))))))) | (~p16(f19(f15(c56)), f28(f19(c56)))) | (~p39(f19(f15(c56)), f19(f11(f13(f5(c44), f14(f5(f6(f7(f7(f6(f6(f7(f7(c44)))))))), f5(c44)))))))),
% 235.61/235.87 inference(modus_ponens,[status(thm)],[183, 182])).
% 235.61/235.87 tff(185,plain,
% 235.61/235.87 ($false),
% 235.61/235.87 inference(unit_resolution,[status(thm)],[184, 178, 168, 165, 151, 86])).
% 235.61/235.87 % SZS output end Proof
% 235.80/235.99 % E exiting
%------------------------------------------------------------------------------