%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN574-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:39:36 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN574-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.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 12:38:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 tff(p2_type, type, (
% 0.19/0.38 p2: ( $i * $i ) > $o)).
% 0.19/0.38 tff(f5_type, type, (
% 0.19/0.38 f5: $i > $i)).
% 0.19/0.38 tff(c14_type, type, (
% 0.19/0.38 c14: $i)).
% 0.19/0.38 tff(p9_type, type, (
% 0.19/0.38 p9: ( $i * $i ) > $o)).
% 0.19/0.38 tff(f4_type, type, (
% 0.19/0.38 f4: $i > $i)).
% 0.19/0.38 tff(f8_type, type, (
% 0.19/0.38 f8: ( $i * $i ) > $i)).
% 0.19/0.38 tff(c12_type, type, (
% 0.19/0.38 c12: $i)).
% 0.19/0.38 tff(p3_type, type, (
% 0.19/0.38 p3: ( $i * $i ) > $o)).
% 0.19/0.38 tff(p7_type, type, (
% 0.19/0.38 p7: ( $i * $i ) > $o)).
% 0.19/0.38 tff(c13_type, type, (
% 0.19/0.38 c13: $i)).
% 0.19/0.38 tff(p11_type, type, (
% 0.19/0.38 p11: ( $i * $i ) > $o)).
% 0.19/0.38 tff(c15_type, type, (
% 0.19/0.38 c15: $i)).
% 0.19/0.38 tff(1,assumption,(p2(f5(c14), f5(c14))), introduced(assumption)).
% 0.19/0.38 tff(2,plain,
% 0.19/0.38 (^[X16: $i, X15: $i] : refl(((~p2(X15, X16)) | p3(f4(X15), f4(X16))) <=> ((~p2(X15, X16)) | p3(f4(X15), f4(X16))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(3,plain,
% 0.19/0.38 (![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16))) <=> ![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.38 tff(4,plain,
% 0.19/0.38 (![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16))) <=> ![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16)))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(5,plain,
% 0.19/0.38 (^[X16: $i, X15: $i] : rewrite((p3(f4(X15), f4(X16)) | (~p2(X15, X16))) <=> ((~p2(X15, X16)) | p3(f4(X15), f4(X16))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(6,plain,
% 0.19/0.38 (![X16: $i, X15: $i] : (p3(f4(X15), f4(X16)) | (~p2(X15, X16))) <=> ![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16)))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.38 tff(7,axiom,(![X16: $i, X15: $i] : (p3(f4(X15), f4(X16)) | (~p2(X15, X16)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_13')).
% 0.19/0.38 tff(8,plain,
% 0.19/0.38 (![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.19/0.38 tff(9,plain,
% 0.19/0.38 (![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.19/0.38 tff(10,plain,(
% 0.19/0.38 ![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16)))),
% 0.19/0.38 inference(skolemize,[status(sab)],[9])).
% 0.19/0.38 tff(11,plain,
% 0.19/0.38 (![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[10, 3])).
% 0.19/0.38 tff(12,plain,
% 0.19/0.38 (((~![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16)))) | ((~p2(f5(c14), f5(c14))) | p3(f4(f5(c14)), f4(f5(c14))))) <=> ((~![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16)))) | (~p2(f5(c14), f5(c14))) | p3(f4(f5(c14)), f4(f5(c14))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(13,plain,
% 0.19/0.38 ((~![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16)))) | ((~p2(f5(c14), f5(c14))) | p3(f4(f5(c14)), f4(f5(c14))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(14,plain,
% 0.19/0.38 ((~![X16: $i, X15: $i] : ((~p2(X15, X16)) | p3(f4(X15), f4(X16)))) | (~p2(f5(c14), f5(c14))) | p3(f4(f5(c14)), f4(f5(c14)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.38 tff(15,plain,
% 0.19/0.38 (p3(f4(f5(c14)), f4(f5(c14)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[14, 11, 1])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (^[X17: $i] : refl(p3(f4(f5(X17)), f4(X17)) <=> p3(f4(f5(X17)), f4(X17)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (![X17: $i] : p3(f4(f5(X17)), f4(X17)) <=> ![X17: $i] : p3(f4(f5(X17)), f4(X17))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![X17: $i] : p3(f4(f5(X17)), f4(X17)) <=> ![X17: $i] : p3(f4(f5(X17)), f4(X17))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(19,axiom,(![X17: $i] : p3(f4(f5(X17)), f4(X17))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_7')).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (![X17: $i] : p3(f4(f5(X17)), f4(X17))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.19/0.38 tff(21,plain,(
% 0.19/0.38 ![X17: $i] : p3(f4(f5(X17)), f4(X17))),
% 0.19/0.38 inference(skolemize,[status(sab)],[20])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (![X17: $i] : p3(f4(f5(X17)), f4(X17))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 ((~![X17: $i] : p3(f4(f5(X17)), f4(X17))) | p3(f4(f5(c14)), f4(c14))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 (p3(f4(f5(c14)), f4(c14))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (^[X14: $i, X12: $i, X13: $i] : refl(((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14)) <=> ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14)) <=> ![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14)) <=> ![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (^[X14: $i, X12: $i, X13: $i] : trans(monotonicity(rewrite((p3(X13, X14) | (~p3(X12, X13))) <=> ((~p3(X12, X13)) | p3(X13, X14))), (((p3(X13, X14) | (~p3(X12, X13))) | (~p3(X12, X14))) <=> (((~p3(X12, X13)) | p3(X13, X14)) | (~p3(X12, X14))))), rewrite((((~p3(X12, X13)) | p3(X13, X14)) | (~p3(X12, X14))) <=> ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))), (((p3(X13, X14) | (~p3(X12, X13))) | (~p3(X12, X14))) <=> ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (![X14: $i, X12: $i, X13: $i] : ((p3(X13, X14) | (~p3(X12, X13))) | (~p3(X12, X14))) <=> ![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.38 tff(30,axiom,(![X14: $i, X12: $i, X13: $i] : ((p3(X13, X14) | (~p3(X12, X13))) | (~p3(X12, X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p3_16')).
% 0.19/0.38 tff(31,plain,
% 0.19/0.38 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.19/0.38 tff(33,plain,(
% 0.19/0.38 ![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.19/0.38 inference(skolemize,[status(sab)],[32])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[33, 26])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 (((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f4(f5(c14)), f4(c14))) | (~p3(f4(f5(c14)), f4(f5(c14)))) | p3(f4(c14), f4(f5(c14))))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | (~p3(f4(f5(c14)), f4(c14))) | (~p3(f4(f5(c14)), f4(f5(c14)))) | p3(f4(c14), f4(f5(c14))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (((~p3(f4(f5(c14)), f4(f5(c14)))) | (~p3(f4(f5(c14)), f4(c14))) | p3(f4(c14), f4(f5(c14)))) <=> ((~p3(f4(f5(c14)), f4(c14))) | (~p3(f4(f5(c14)), f4(f5(c14)))) | p3(f4(c14), f4(f5(c14))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f4(f5(c14)), f4(f5(c14)))) | (~p3(f4(f5(c14)), f4(c14))) | p3(f4(c14), f4(f5(c14))))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f4(f5(c14)), f4(c14))) | (~p3(f4(f5(c14)), f4(f5(c14)))) | p3(f4(c14), f4(f5(c14)))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f4(f5(c14)), f4(f5(c14)))) | (~p3(f4(f5(c14)), f4(c14))) | p3(f4(c14), f4(f5(c14))))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | (~p3(f4(f5(c14)), f4(c14))) | (~p3(f4(f5(c14)), f4(f5(c14)))) | p3(f4(c14), f4(f5(c14))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[37, 35])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | ((~p3(f4(f5(c14)), f4(f5(c14)))) | (~p3(f4(f5(c14)), f4(c14))) | p3(f4(c14), f4(f5(c14))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 ((~![X14: $i, X12: $i, X13: $i] : ((~p3(X12, X14)) | (~p3(X12, X13)) | p3(X13, X14))) | (~p3(f4(f5(c14)), f4(c14))) | (~p3(f4(f5(c14)), f4(f5(c14)))) | p3(f4(c14), f4(f5(c14)))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (p3(f4(c14), f4(f5(c14)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[40, 34, 24, 15])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (^[X21: $i] : refl(p7(X21, X21) <=> p7(X21, X21))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(43,plain,
% 0.19/0.38 (![X21: $i] : p7(X21, X21) <=> ![X21: $i] : p7(X21, X21)),
% 0.19/0.38 inference(quant_intro,[status(thm)],[42])).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (![X21: $i] : p7(X21, X21) <=> ![X21: $i] : p7(X21, X21)),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(45,axiom,(![X21: $i] : p7(X21, X21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_2')).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (![X21: $i] : p7(X21, X21)),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.38 tff(47,plain,(
% 0.19/0.38 ![X21: $i] : p7(X21, X21)),
% 0.19/0.38 inference(skolemize,[status(sab)],[46])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (![X21: $i] : p7(X21, X21)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 ((~![X21: $i] : p7(X21, X21)) | p7(c12, c12)),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (p7(c12, c12)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.19/0.39 tff(51,plain,
% 0.19/0.39 (^[X32: $i] : refl((p9(X32, f4(c14)) | (~p9(X32, c13))) <=> (p9(X32, f4(c14)) | (~p9(X32, c13))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![X32: $i] : (p9(X32, f4(c14)) | (~p9(X32, c13))) <=> ![X32: $i] : (p9(X32, f4(c14)) | (~p9(X32, c13)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (![X32: $i] : (p9(X32, f4(c14)) | (~p9(X32, c13))) <=> ![X32: $i] : (p9(X32, f4(c14)) | (~p9(X32, c13)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(54,axiom,(![X32: $i] : (p9(X32, f4(c14)) | (~p9(X32, c13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_10')).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (![X32: $i] : (p9(X32, f4(c14)) | (~p9(X32, c13)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.19/0.39 tff(56,plain,(
% 0.19/0.39 ![X32: $i] : (p9(X32, f4(c14)) | (~p9(X32, c13)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[55])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 (![X32: $i] : (p9(X32, f4(c14)) | (~p9(X32, c13)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 (p9(c12, c13) <=> p9(c12, c13)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(59,axiom,(p9(c12, c13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_5')).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (p9(c12, c13)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (((~![X32: $i] : (p9(X32, f4(c14)) | (~p9(X32, c13)))) | (p9(c12, f4(c14)) | (~p9(c12, c13)))) <=> ((~![X32: $i] : (p9(X32, f4(c14)) | (~p9(X32, c13)))) | p9(c12, f4(c14)) | (~p9(c12, c13)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 ((~![X32: $i] : (p9(X32, f4(c14)) | (~p9(X32, c13)))) | (p9(c12, f4(c14)) | (~p9(c12, c13)))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 ((~![X32: $i] : (p9(X32, f4(c14)) | (~p9(X32, c13)))) | p9(c12, f4(c14)) | (~p9(c12, c13))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (p9(c12, f4(c14))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[63, 60, 57])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (^[X31: $i, X30: $i, X29: $i, X28: $i] : refl(((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) <=> ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) <=> ![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.39 tff(67,plain,
% 0.19/0.39 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) <=> ![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (^[X31: $i, X30: $i, X29: $i, X28: $i] : trans(monotonicity(trans(monotonicity(rewrite((p9(X28, X29) | (~p7(X31, X28))) <=> ((~p7(X31, X28)) | p9(X28, X29))), (((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) <=> (((~p7(X31, X28)) | p9(X28, X29)) | (~p9(X31, X30))))), rewrite((((~p7(X31, X28)) | p9(X28, X29)) | (~p9(X31, X30))) <=> ((~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))), (((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) <=> ((~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)))), ((((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) | (~p3(X30, X29))) <=> (((~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) | (~p3(X30, X29))))), rewrite((((~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29)) | (~p3(X30, X29))) <=> ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))), ((((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) | (~p3(X30, X29))) <=> ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (![X31: $i, X30: $i, X29: $i, X28: $i] : (((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) | (~p3(X30, X29))) <=> ![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.39 tff(70,axiom,(![X31: $i, X30: $i, X29: $i, X28: $i] : (((p9(X28, X29) | (~p7(X31, X28))) | (~p9(X31, X30))) | (~p3(X30, X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_19')).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.39 tff(73,plain,(
% 0.19/0.39 ![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.19/0.39 inference(skolemize,[status(sab)],[72])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | (p9(c12, f4(f5(c14))) | (~p3(f4(c14), f4(f5(c14)))) | (~p7(c12, c12)) | (~p9(c12, f4(c14))))) <=> ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | p9(c12, f4(f5(c14))) | (~p3(f4(c14), f4(f5(c14)))) | (~p7(c12, c12)) | (~p9(c12, f4(c14))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 (((~p3(f4(c14), f4(f5(c14)))) | (~p9(c12, f4(c14))) | (~p7(c12, c12)) | p9(c12, f4(f5(c14)))) <=> (p9(c12, f4(f5(c14))) | (~p3(f4(c14), f4(f5(c14)))) | (~p7(c12, c12)) | (~p9(c12, f4(c14))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f4(c14), f4(f5(c14)))) | (~p9(c12, f4(c14))) | (~p7(c12, c12)) | p9(c12, f4(f5(c14))))) <=> ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | (p9(c12, f4(f5(c14))) | (~p3(f4(c14), f4(f5(c14)))) | (~p7(c12, c12)) | (~p9(c12, f4(c14)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[76])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f4(c14), f4(f5(c14)))) | (~p9(c12, f4(c14))) | (~p7(c12, c12)) | p9(c12, f4(f5(c14))))) <=> ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | p9(c12, f4(f5(c14))) | (~p3(f4(c14), f4(f5(c14)))) | (~p7(c12, c12)) | (~p9(c12, f4(c14))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[77, 75])).
% 0.19/0.39 tff(79,plain,
% 0.19/0.39 ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | ((~p3(f4(c14), f4(f5(c14)))) | (~p9(c12, f4(c14))) | (~p7(c12, c12)) | p9(c12, f4(f5(c14))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 ((~![X31: $i, X30: $i, X29: $i, X28: $i] : ((~p3(X30, X29)) | (~p9(X31, X30)) | (~p7(X31, X28)) | p9(X28, X29))) | p9(c12, f4(f5(c14))) | (~p3(f4(c14), f4(f5(c14)))) | (~p7(c12, c12)) | (~p9(c12, f4(c14)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 (p9(c12, f4(f5(c14)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[80, 74, 64, 50, 41])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (^[X35: $i, X34: $i, X33: $i] : refl(((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33))) <=> ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[82])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33))) <=> ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (^[X35: $i, X34: $i, X33: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)))), (((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) | (~p9(f8(X33, X34), X33))) <=> (((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15))) | (~p9(f8(X33, X34), X33))))), rewrite((((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15))) | (~p9(f8(X33, X34), X33))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), X33)))), (((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) | (~p9(f8(X33, X34), X33))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), X33))))), ((((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f4(X34)))) <=> (((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f4(X34)))))), rewrite((((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f4(X34)))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))), ((((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f4(X34)))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (![X35: $i, X34: $i, X33: $i] : (((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f4(X34)))) <=> ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.39 tff(87,axiom,(![X35: $i, X34: $i, X33: $i] : (((((~p11(X35, c15)) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) | (~p9(f8(X33, X34), X33))) | (~p9(f8(X33, X34), f4(X34))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p11_22')).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.19/0.39 tff(90,plain,(
% 0.19/0.39 ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.39 inference(skolemize,[status(sab)],[89])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 (p11(c14, c15) <=> p11(c14, c15)),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(93,axiom,(p11(c14, c15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_6')).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 (p11(c14, c15)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 (((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))) | (~p11(c14, c15)))) <=> ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))) | (~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))) | (~p11(c14, c15)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 (((~p2(f5(c14), f5(c14))) | (~p9(c12, f4(f5(c14)))) | (~p11(c14, c15)) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))))) <=> ((~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))) | (~p11(c14, c15)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 (((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p2(f5(c14), f5(c14))) | (~p9(c12, f4(f5(c14)))) | (~p11(c14, c15)) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))))) <=> ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))) | (~p11(c14, c15))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[96])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 (((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p2(f5(c14), f5(c14))) | (~p9(c12, f4(f5(c14)))) | (~p11(c14, c15)) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))))) <=> ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))) | (~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))) | (~p11(c14, c15)))),
% 0.19/0.39 inference(transitivity,[status(thm)],[97, 95])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))) | ((~p2(f5(c14), f5(c14))) | (~p9(c12, f4(f5(c14)))) | (~p11(c14, c15)) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | (~p9(f8(X33, X34), f4(X34))) | (~p9(f8(X33, X34), X33)))) | (~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))) | (~p11(c14, c15))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 ((~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[100, 94, 91])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 (~p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[101, 81, 1])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (^[X35: $i, X34: $i, X33: $i] : refl(((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33)) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33)) <=> ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[103])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33)) <=> ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (^[X35: $i, X34: $i, X33: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f4(X34))) <=> (p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))), (((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f4(X34))) | (~p11(X35, c15))) <=> ((p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33)) | (~p11(X35, c15))))), rewrite(((p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33)) | (~p11(X35, c15))) <=> ((~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))), (((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f4(X34))) | (~p11(X35, c15))) <=> ((~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33)))), ((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f4(X34))) | (~p11(X35, c15))) | (~p9(c12, X33))) <=> (((~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33)) | (~p9(c12, X33))))), rewrite((((~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33)) | (~p9(c12, X33))) <=> ((~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))), ((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f4(X34))) | (~p11(X35, c15))) | (~p9(c12, X33))) <=> ((~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33)))), (((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f4(X34))) | (~p11(X35, c15))) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) <=> (((~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33)) | (~p2(X34, f5(X35)))))), rewrite((((~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33)) | (~p2(X34, f5(X35)))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))), (((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f4(X34))) | (~p11(X35, c15))) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) <=> ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (![X35: $i, X34: $i, X33: $i] : ((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f4(X34))) | (~p11(X35, c15))) | (~p9(c12, X33))) | (~p2(X34, f5(X35)))) <=> ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[106])).
% 0.19/0.40 tff(108,axiom,(![X35: $i, X34: $i, X33: $i] : ((((p9(f8(X33, X34), X33) | p9(f8(X33, X34), f4(X34))) | (~p11(X35, c15))) | (~p9(c12, X33))) | (~p2(X34, f5(X35))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_21')).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.19/0.40 tff(111,plain,(
% 0.19/0.40 ![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))),
% 0.19/0.40 inference(skolemize,[status(sab)],[110])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))) | ((~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))) | (~p11(c14, c15)))) <=> ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))) | (~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))) | (~p11(c14, c15)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (((~p2(f5(c14), f5(c14))) | (~p9(c12, f4(f5(c14)))) | (~p11(c14, c15)) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14)))) <=> ((~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))) | (~p11(c14, c15)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))) | ((~p2(f5(c14), f5(c14))) | (~p9(c12, f4(f5(c14)))) | (~p11(c14, c15)) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))))) <=> ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))) | ((~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))) | (~p11(c14, c15))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[114])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 (((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))) | ((~p2(f5(c14), f5(c14))) | (~p9(c12, f4(f5(c14)))) | (~p11(c14, c15)) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))))) <=> ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))) | (~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))) | (~p11(c14, c15)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[115, 113])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))) | ((~p2(f5(c14), f5(c14))) | (~p9(c12, f4(f5(c14)))) | (~p11(c14, c15)) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 ((~![X35: $i, X34: $i, X33: $i] : ((~p2(X34, f5(X35))) | (~p9(c12, X33)) | (~p11(X35, c15)) | p9(f8(X33, X34), f4(X34)) | p9(f8(X33, X34), X33))) | (~p9(c12, f4(f5(c14)))) | (~p2(f5(c14), f5(c14))) | p9(f8(f4(f5(c14)), f5(c14)), f4(f5(c14))) | (~p11(c14, c15))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[118, 94, 112, 1, 81, 102])).
% 0.19/0.40 tff(120,plain,(~p2(f5(c14), f5(c14))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 (^[X7: $i] : refl(p2(X7, X7) <=> p2(X7, X7))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 (![X7: $i] : p2(X7, X7) <=> ![X7: $i] : p2(X7, X7)),
% 0.19/0.40 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 (![X7: $i] : p2(X7, X7) <=> ![X7: $i] : p2(X7, X7)),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(124,axiom,(![X7: $i] : p2(X7, X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_4')).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 (![X7: $i] : p2(X7, X7)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.40 tff(126,plain,(
% 0.19/0.40 ![X7: $i] : p2(X7, X7)),
% 0.19/0.40 inference(skolemize,[status(sab)],[125])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 (![X7: $i] : p2(X7, X7)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 ((~![X7: $i] : p2(X7, X7)) | p2(f5(c14), f5(c14))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(129,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[128, 127, 120])).
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40 % E exiting
%------------------------------------------------------------------------------