%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN561-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:39:35 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SYN561-1 : TPTP v9.0.0. Released v2.5.0.
% 0.01/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 12:40:12 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.37 % SZS status Unsatisfiable
% 0.20/0.37 % SZS output start Proof
% 0.20/0.37 tff(p2_type, type, (
% 0.20/0.37 p2: ( $i * $i ) > $o)).
% 0.20/0.37 tff(f3_type, type, (
% 0.20/0.37 f3: ( $i * $i ) > $i)).
% 0.20/0.37 tff(c13_type, type, (
% 0.20/0.37 c13: $i)).
% 0.20/0.37 tff(f4_type, type, (
% 0.20/0.37 f4: $i > $i)).
% 0.20/0.37 tff(f5_type, type, (
% 0.20/0.37 f5: $i > $i)).
% 0.20/0.37 tff(c12_type, type, (
% 0.20/0.37 c12: $i)).
% 0.20/0.37 tff(c16_type, type, (
% 0.20/0.37 c16: $i)).
% 0.20/0.37 tff(f6_type, type, (
% 0.20/0.37 f6: ( $i * $i ) > $i)).
% 0.20/0.37 tff(c11_type, type, (
% 0.20/0.37 c11: $i)).
% 0.20/0.37 tff(c15_type, type, (
% 0.20/0.37 c15: $i)).
% 0.20/0.37 tff(f7_type, type, (
% 0.20/0.37 f7: ( $i * $i ) > $i)).
% 0.20/0.37 tff(c14_type, type, (
% 0.20/0.37 c14: $i)).
% 0.20/0.37 tff(c10_type, type, (
% 0.20/0.37 c10: $i)).
% 0.20/0.37 tff(p9_type, type, (
% 0.20/0.37 p9: ( $i * $i ) > $o)).
% 0.20/0.37 tff(p8_type, type, (
% 0.20/0.37 p8: ( $i * $i ) > $o)).
% 0.20/0.37 tff(1,assumption,(~p2(c13, c13)), introduced(assumption)).
% 0.20/0.37 tff(2,plain,
% 0.20/0.37 (^[X0: $i] : refl(p2(X0, X0) <=> p2(X0, X0))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(3,plain,
% 0.20/0.37 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.20/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.37 tff(4,plain,
% 0.20/0.37 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(5,axiom,(![X0: $i] : p2(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_1')).
% 0.20/0.37 tff(6,plain,
% 0.20/0.37 (![X0: $i] : p2(X0, X0)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.37 tff(7,plain,(
% 0.20/0.37 ![X0: $i] : p2(X0, X0)),
% 0.20/0.37 inference(skolemize,[status(sab)],[6])).
% 0.20/0.37 tff(8,plain,
% 0.20/0.37 (![X0: $i] : p2(X0, X0)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.37 tff(9,plain,
% 0.20/0.37 ((~![X0: $i] : p2(X0, X0)) | p2(c13, c13)),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(10,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.37 tff(11,plain,(p2(c13, c13)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(12,assumption,(~p2(f5(c12), f5(c12))), introduced(assumption)).
% 0.20/0.37 tff(13,plain,
% 0.20/0.37 ((~![X0: $i] : p2(X0, X0)) | p2(f5(c12), f5(c12))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(14,plain,
% 0.20/0.37 ($false),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[13, 8, 12])).
% 0.20/0.37 tff(15,plain,(p2(f5(c12), f5(c12))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.37 tff(16,plain,
% 0.20/0.37 (^[X7: $i, X8: $i] : refl(((~p2(X7, X8)) | p2(f4(X7), f4(X8))) <=> ((~p2(X7, X8)) | p2(f4(X7), f4(X8))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(17,plain,
% 0.20/0.37 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8))) <=> ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.37 tff(18,plain,
% 0.20/0.37 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8))) <=> ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(19,plain,
% 0.20/0.37 (^[X7: $i, X8: $i] : rewrite((p2(f4(X7), f4(X8)) | (~p2(X7, X8))) <=> ((~p2(X7, X8)) | p2(f4(X7), f4(X8))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(20,plain,
% 0.20/0.37 (![X7: $i, X8: $i] : (p2(f4(X7), f4(X8)) | (~p2(X7, X8))) <=> ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.37 tff(21,axiom,(![X7: $i, X8: $i] : (p2(f4(X7), f4(X8)) | (~p2(X7, X8)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_8')).
% 0.20/0.37 tff(22,plain,
% 0.20/0.37 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.37 tff(23,plain,
% 0.20/0.37 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.37 tff(24,plain,(
% 0.20/0.37 ![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[23])).
% 0.20/0.37 tff(25,plain,
% 0.20/0.37 (![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.20/0.37 tff(26,plain,
% 0.20/0.37 (((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))) | ((~p2(f5(c12), f5(c12))) | p2(f4(f5(c12)), f4(f5(c12))))) <=> ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))) | (~p2(f5(c12), f5(c12))) | p2(f4(f5(c12)), f4(f5(c12))))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(27,plain,
% 0.20/0.37 ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))) | ((~p2(f5(c12), f5(c12))) | p2(f4(f5(c12)), f4(f5(c12))))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(28,plain,
% 0.20/0.37 ((~![X7: $i, X8: $i] : ((~p2(X7, X8)) | p2(f4(X7), f4(X8)))) | (~p2(f5(c12), f5(c12))) | p2(f4(f5(c12)), f4(f5(c12)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.37 tff(29,plain,
% 0.20/0.37 ((~p2(f5(c12), f5(c12))) | p2(f4(f5(c12)), f4(f5(c12)))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.20/0.37 tff(30,plain,
% 0.20/0.37 (p2(f4(f5(c12)), f4(f5(c12)))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[29, 15])).
% 0.20/0.37 tff(31,plain,
% 0.20/0.37 (^[X6: $i, X4: $i, X3: $i, X5: $i] : refl(((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6))) <=> ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(32,plain,
% 0.20/0.37 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.37 tff(33,plain,
% 0.20/0.37 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(34,plain,
% 0.20/0.37 (^[X6: $i, X4: $i, X3: $i, X5: $i] : trans(monotonicity(rewrite((p2(f3(X3, X4), f3(X5, X6)) | (~p2(X3, X5))) <=> ((~p2(X3, X5)) | p2(f3(X3, X4), f3(X5, X6)))), (((p2(f3(X3, X4), f3(X5, X6)) | (~p2(X3, X5))) | (~p2(X4, X6))) <=> (((~p2(X3, X5)) | p2(f3(X3, X4), f3(X5, X6))) | (~p2(X4, X6))))), rewrite((((~p2(X3, X5)) | p2(f3(X3, X4), f3(X5, X6))) | (~p2(X4, X6))) <=> ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))), (((p2(f3(X3, X4), f3(X5, X6)) | (~p2(X3, X5))) | (~p2(X4, X6))) <=> ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(35,plain,
% 0.20/0.37 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((p2(f3(X3, X4), f3(X5, X6)) | (~p2(X3, X5))) | (~p2(X4, X6))) <=> ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.37 tff(36,axiom,(![X6: $i, X4: $i, X3: $i, X5: $i] : ((p2(f3(X3, X4), f3(X5, X6)) | (~p2(X3, X5))) | (~p2(X4, X6)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_12')).
% 0.20/0.37 tff(37,plain,
% 0.20/0.37 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.37 tff(38,plain,
% 0.20/0.37 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.37 tff(39,plain,(
% 0.20/0.37 ![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.20/0.37 inference(skolemize,[status(sab)],[38])).
% 0.20/0.37 tff(40,plain,
% 0.20/0.37 (![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.37 tff(41,plain,
% 0.20/0.37 (((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))) | ((~p2(f4(f5(c12)), f4(f5(c12)))) | (~p2(c13, c13)) | p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13)))) <=> ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))) | (~p2(f4(f5(c12)), f4(f5(c12)))) | (~p2(c13, c13)) | p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(42,plain,
% 0.20/0.37 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))) | ((~p2(f4(f5(c12)), f4(f5(c12)))) | (~p2(c13, c13)) | p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13)))),
% 0.20/0.37 inference(quant_inst,[status(thm)],[])).
% 0.20/0.37 tff(43,plain,
% 0.20/0.37 ((~![X6: $i, X4: $i, X3: $i, X5: $i] : ((~p2(X3, X5)) | (~p2(X4, X6)) | p2(f3(X3, X4), f3(X5, X6)))) | (~p2(f4(f5(c12)), f4(f5(c12)))) | (~p2(c13, c13)) | p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.37 tff(44,plain,
% 0.20/0.37 ((~p2(f4(f5(c12)), f4(f5(c12)))) | (~p2(c13, c13)) | p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.20/0.37 tff(45,plain,
% 0.20/0.37 ((~p2(c13, c13)) | p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[44, 30])).
% 0.20/0.37 tff(46,plain,
% 0.20/0.37 (p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))),
% 0.20/0.37 inference(unit_resolution,[status(thm)],[45, 11])).
% 0.20/0.37 tff(47,plain,
% 0.20/0.37 (^[X0: $i, X2: $i, X1: $i] : refl(((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2)) <=> ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2)))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(48,plain,
% 0.20/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.37 tff(49,plain,
% 0.20/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(50,plain,
% 0.20/0.37 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p2(X1, X2) | (~p2(X0, X1))) <=> ((~p2(X0, X1)) | p2(X1, X2))), (((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2))) <=> (((~p2(X0, X1)) | p2(X1, X2)) | (~p2(X0, X2))))), rewrite((((~p2(X0, X1)) | p2(X1, X2)) | (~p2(X0, X2))) <=> ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))), (((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2))) <=> ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))))),
% 0.20/0.37 inference(bind,[status(th)],[])).
% 0.20/0.37 tff(51,plain,
% 0.20/0.37 (![X0: $i, X2: $i, X1: $i] : ((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.20/0.37 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.37 tff(52,axiom,(![X0: $i, X2: $i, X1: $i] : ((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_9')).
% 0.20/0.37 tff(53,plain,
% 0.20/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.37 tff(54,plain,
% 0.20/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.37 tff(55,plain,(
% 0.20/0.37 ![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.20/0.37 inference(skolemize,[status(sab)],[54])).
% 0.20/0.37 tff(56,plain,
% 0.20/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.37 tff(57,plain,
% 0.20/0.37 (p2(f3(f4(f5(c12)), c13), c16) <=> p2(f3(f4(f5(c12)), c13), c16)),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(58,axiom,(p2(f3(f4(f5(c12)), c13), c16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_6')).
% 0.20/0.37 tff(59,plain,
% 0.20/0.37 (p2(f3(f4(f5(c12)), c13), c16)),
% 0.20/0.37 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.37 tff(60,plain,
% 0.20/0.37 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(f4(f5(c12)), c13), c16)) | (~p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))) | p2(c16, f3(f4(f5(c12)), c13)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f3(f4(f5(c12)), c13), c16)) | (~p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))) | p2(c16, f3(f4(f5(c12)), c13)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(61,plain,
% 0.20/0.37 (((~p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))) | (~p2(f3(f4(f5(c12)), c13), c16)) | p2(c16, f3(f4(f5(c12)), c13))) <=> ((~p2(f3(f4(f5(c12)), c13), c16)) | (~p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))) | p2(c16, f3(f4(f5(c12)), c13)))),
% 0.20/0.37 inference(rewrite,[status(thm)],[])).
% 0.20/0.37 tff(62,plain,
% 0.20/0.37 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))) | (~p2(f3(f4(f5(c12)), c13), c16)) | p2(c16, f3(f4(f5(c12)), c13)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(f4(f5(c12)), c13), c16)) | (~p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))) | p2(c16, f3(f4(f5(c12)), c13))))),
% 0.20/0.37 inference(monotonicity,[status(thm)],[61])).
% 0.20/0.37 tff(63,plain,
% 0.20/0.37 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))) | (~p2(f3(f4(f5(c12)), c13), c16)) | p2(c16, f3(f4(f5(c12)), c13)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f3(f4(f5(c12)), c13), c16)) | (~p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))) | p2(c16, f3(f4(f5(c12)), c13)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[62, 60])).
% 0.20/0.38 tff(64,plain,
% 0.20/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))) | (~p2(f3(f4(f5(c12)), c13), c16)) | p2(c16, f3(f4(f5(c12)), c13)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(65,plain,
% 0.20/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f3(f4(f5(c12)), c13), c16)) | (~p2(f3(f4(f5(c12)), c13), f3(f4(f5(c12)), c13))) | p2(c16, f3(f4(f5(c12)), c13))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.38 tff(66,plain,
% 0.20/0.38 (p2(c16, f3(f4(f5(c12)), c13))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[65, 59, 56, 46])).
% 0.20/0.38 tff(67,assumption,(~p2(c11, c11)), introduced(assumption)).
% 0.20/0.38 tff(68,plain,
% 0.20/0.38 ((~![X0: $i] : p2(X0, X0)) | p2(c11, c11)),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(69,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[68, 8, 67])).
% 0.20/0.38 tff(70,plain,(p2(c11, c11)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(71,plain,
% 0.20/0.38 (p2(f7(c10, c14), c15) <=> p2(f7(c10, c14), c15)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(72,axiom,(p2(f7(c10, c14), c15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_4')).
% 0.20/0.38 tff(73,plain,
% 0.20/0.38 (p2(f7(c10, c14), c15)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.38 tff(74,plain,
% 0.20/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f7(c10, c14), c15)) | p2(c15, c15))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f7(c10, c14), c15)) | p2(c15, c15))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(75,plain,
% 0.20/0.38 (((~p2(f7(c10, c14), c15)) | (~p2(f7(c10, c14), c15)) | p2(c15, c15)) <=> ((~p2(f7(c10, c14), c15)) | p2(c15, c15))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(76,plain,
% 0.20/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f7(c10, c14), c15)) | (~p2(f7(c10, c14), c15)) | p2(c15, c15))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f7(c10, c14), c15)) | p2(c15, c15)))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[75])).
% 0.20/0.38 tff(77,plain,
% 0.20/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f7(c10, c14), c15)) | (~p2(f7(c10, c14), c15)) | p2(c15, c15))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f7(c10, c14), c15)) | p2(c15, c15))),
% 0.20/0.38 inference(transitivity,[status(thm)],[76, 74])).
% 0.20/0.38 tff(78,plain,
% 0.20/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f7(c10, c14), c15)) | (~p2(f7(c10, c14), c15)) | p2(c15, c15))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(79,plain,
% 0.20/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f7(c10, c14), c15)) | p2(c15, c15)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.38 tff(80,plain,
% 0.20/0.38 (p2(c15, c15)),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[79, 73, 56])).
% 0.20/0.38 tff(81,plain,
% 0.20/0.38 (^[X14: $i, X12: $i, X11: $i, X13: $i] : refl(((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14))) <=> ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(82,plain,
% 0.20/0.38 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14))) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.38 tff(83,plain,
% 0.20/0.38 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14))) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(84,plain,
% 0.20/0.38 (^[X14: $i, X12: $i, X11: $i, X13: $i] : trans(monotonicity(rewrite((p2(f6(X11, X12), f6(X13, X14)) | (~p2(X12, X14))) <=> ((~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))), (((p2(f6(X11, X12), f6(X13, X14)) | (~p2(X12, X14))) | (~p2(X11, X13))) <=> (((~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14))) | (~p2(X11, X13))))), rewrite((((~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14))) | (~p2(X11, X13))) <=> ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))), (((p2(f6(X11, X12), f6(X13, X14)) | (~p2(X12, X14))) | (~p2(X11, X13))) <=> ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(85,plain,
% 0.20/0.38 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((p2(f6(X11, X12), f6(X13, X14)) | (~p2(X12, X14))) | (~p2(X11, X13))) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.38 tff(86,axiom,(![X14: $i, X12: $i, X11: $i, X13: $i] : ((p2(f6(X11, X12), f6(X13, X14)) | (~p2(X12, X14))) | (~p2(X11, X13)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_14')).
% 0.20/0.38 tff(87,plain,
% 0.20/0.38 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.38 tff(88,plain,
% 0.20/0.38 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.20/0.38 tff(89,plain,(
% 0.20/0.38 ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))),
% 0.20/0.38 inference(skolemize,[status(sab)],[88])).
% 0.20/0.38 tff(90,plain,
% 0.20/0.38 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.20/0.38 tff(91,plain,
% 0.20/0.38 (((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))) | ((~p2(c15, c15)) | (~p2(c11, c11)) | p2(f6(c15, c11), f6(c15, c11)))) <=> ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))) | (~p2(c15, c15)) | (~p2(c11, c11)) | p2(f6(c15, c11), f6(c15, c11)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(92,plain,
% 0.20/0.38 ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))) | ((~p2(c15, c15)) | (~p2(c11, c11)) | p2(f6(c15, c11), f6(c15, c11)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(93,plain,
% 0.20/0.38 ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p2(X11, X13)) | (~p2(X12, X14)) | p2(f6(X11, X12), f6(X13, X14)))) | (~p2(c15, c15)) | (~p2(c11, c11)) | p2(f6(c15, c11), f6(c15, c11))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.38 tff(94,plain,
% 0.20/0.38 ((~p2(c11, c11)) | p2(f6(c15, c11), f6(c15, c11))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[93, 90, 80])).
% 0.20/0.38 tff(95,plain,
% 0.20/0.38 (p2(f6(c15, c11), f6(c15, c11))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[94, 70])).
% 0.20/0.38 tff(96,plain,
% 0.20/0.38 (p2(f6(c15, c11), c16) <=> p2(f6(c15, c11), c16)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(97,axiom,(p2(f6(c15, c11), c16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_5')).
% 0.20/0.38 tff(98,plain,
% 0.20/0.38 (p2(f6(c15, c11), c16)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.38 tff(99,plain,
% 0.20/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f6(c15, c11), c16)) | (~p2(f6(c15, c11), f6(c15, c11))) | p2(c16, f6(c15, c11)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f6(c15, c11), c16)) | (~p2(f6(c15, c11), f6(c15, c11))) | p2(c16, f6(c15, c11)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(100,plain,
% 0.20/0.38 (((~p2(f6(c15, c11), f6(c15, c11))) | (~p2(f6(c15, c11), c16)) | p2(c16, f6(c15, c11))) <=> ((~p2(f6(c15, c11), c16)) | (~p2(f6(c15, c11), f6(c15, c11))) | p2(c16, f6(c15, c11)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(101,plain,
% 0.20/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f6(c15, c11), f6(c15, c11))) | (~p2(f6(c15, c11), c16)) | p2(c16, f6(c15, c11)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f6(c15, c11), c16)) | (~p2(f6(c15, c11), f6(c15, c11))) | p2(c16, f6(c15, c11))))),
% 0.20/0.38 inference(monotonicity,[status(thm)],[100])).
% 0.20/0.38 tff(102,plain,
% 0.20/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f6(c15, c11), f6(c15, c11))) | (~p2(f6(c15, c11), c16)) | p2(c16, f6(c15, c11)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f6(c15, c11), c16)) | (~p2(f6(c15, c11), f6(c15, c11))) | p2(c16, f6(c15, c11)))),
% 0.20/0.38 inference(transitivity,[status(thm)],[101, 99])).
% 0.20/0.38 tff(103,plain,
% 0.20/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f6(c15, c11), f6(c15, c11))) | (~p2(f6(c15, c11), c16)) | p2(c16, f6(c15, c11)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(104,plain,
% 0.20/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f6(c15, c11), c16)) | (~p2(f6(c15, c11), f6(c15, c11))) | p2(c16, f6(c15, c11))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.38 tff(105,plain,
% 0.20/0.38 (p2(c16, f6(c15, c11))),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[104, 98, 56, 95])).
% 0.20/0.38 tff(106,plain,
% 0.20/0.38 (^[X27: $i, X28: $i] : refl(((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10))) <=> ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(107,plain,
% 0.20/0.38 (![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10))) <=> ![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.38 tff(108,plain,
% 0.20/0.38 (![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10))) <=> ![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(109,plain,
% 0.20/0.38 (^[X27: $i, X28: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~p9(X28, c10)) | (~p8(c11, X28))) <=> ((~p8(c11, X28)) | (~p9(X28, c10)))), ((((~p9(X28, c10)) | (~p8(c11, X28))) | (~p2(f7(c10, X28), X27))) <=> (((~p8(c11, X28)) | (~p9(X28, c10))) | (~p2(f7(c10, X28), X27))))), rewrite((((~p8(c11, X28)) | (~p9(X28, c10))) | (~p2(f7(c10, X28), X27))) <=> ((~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))), ((((~p9(X28, c10)) | (~p8(c11, X28))) | (~p2(f7(c10, X28), X27))) <=> ((~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10))))), (((((~p9(X28, c10)) | (~p8(c11, X28))) | (~p2(f7(c10, X28), X27))) | (~p2(f6(X27, c11), f3(f4(f5(c12)), c13)))) <=> (((~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10))) | (~p2(f6(X27, c11), f3(f4(f5(c12)), c13)))))), rewrite((((~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10))) | (~p2(f6(X27, c11), f3(f4(f5(c12)), c13)))) <=> ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))), (((((~p9(X28, c10)) | (~p8(c11, X28))) | (~p2(f7(c10, X28), X27))) | (~p2(f6(X27, c11), f3(f4(f5(c12)), c13)))) <=> ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(110,plain,
% 0.20/0.38 (![X27: $i, X28: $i] : ((((~p9(X28, c10)) | (~p8(c11, X28))) | (~p2(f7(c10, X28), X27))) | (~p2(f6(X27, c11), f3(f4(f5(c12)), c13)))) <=> ![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.38 tff(111,axiom,(![X27: $i, X28: $i] : ((((~p9(X28, c10)) | (~p8(c11, X28))) | (~p2(f7(c10, X28), X27))) | (~p2(f6(X27, c11), f3(f4(f5(c12)), c13))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p9_15')).
% 0.20/0.39 tff(112,plain,
% 0.20/0.39 (![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.39 tff(113,plain,
% 0.20/0.39 (![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.20/0.39 tff(114,plain,(
% 0.20/0.39 ![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[113])).
% 0.20/0.39 tff(115,plain,
% 0.20/0.39 (![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.20/0.39 tff(116,plain,
% 0.20/0.39 (p8(c11, c14) <=> p8(c11, c14)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(117,axiom,(p8(c11, c14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_3')).
% 0.20/0.39 tff(118,plain,
% 0.20/0.39 (p8(c11, c14)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.39 tff(119,plain,
% 0.20/0.39 (p9(c14, c10) <=> p9(c14, c10)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(120,axiom,(p9(c14, c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_2')).
% 0.20/0.39 tff(121,plain,
% 0.20/0.39 (p9(c14, c10)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.39 tff(122,plain,
% 0.20/0.39 (((~![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))) | ((~p2(f6(c15, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, c14), c15)) | (~p8(c11, c14)) | (~p9(c14, c10)))) <=> ((~![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))) | (~p2(f6(c15, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, c14), c15)) | (~p8(c11, c14)) | (~p9(c14, c10)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(123,plain,
% 0.20/0.39 ((~![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))) | ((~p2(f6(c15, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, c14), c15)) | (~p8(c11, c14)) | (~p9(c14, c10)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(124,plain,
% 0.20/0.39 ((~![X27: $i, X28: $i] : ((~p2(f6(X27, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, X28), X27)) | (~p8(c11, X28)) | (~p9(X28, c10)))) | (~p2(f6(c15, c11), f3(f4(f5(c12)), c13))) | (~p2(f7(c10, c14), c15)) | (~p8(c11, c14)) | (~p9(c14, c10))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.39 tff(125,plain,
% 0.20/0.39 (~p2(f6(c15, c11), f3(f4(f5(c12)), c13))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[124, 121, 118, 73, 115])).
% 0.20/0.39 tff(126,plain,
% 0.20/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (p2(f6(c15, c11), f3(f4(f5(c12)), c13)) | (~p2(c16, f6(c15, c11))) | (~p2(c16, f3(f4(f5(c12)), c13))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | p2(f6(c15, c11), f3(f4(f5(c12)), c13)) | (~p2(c16, f6(c15, c11))) | (~p2(c16, f3(f4(f5(c12)), c13))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(127,plain,
% 0.20/0.39 (((~p2(c16, f3(f4(f5(c12)), c13))) | (~p2(c16, f6(c15, c11))) | p2(f6(c15, c11), f3(f4(f5(c12)), c13))) <=> (p2(f6(c15, c11), f3(f4(f5(c12)), c13)) | (~p2(c16, f6(c15, c11))) | (~p2(c16, f3(f4(f5(c12)), c13))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(128,plain,
% 0.20/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c16, f3(f4(f5(c12)), c13))) | (~p2(c16, f6(c15, c11))) | p2(f6(c15, c11), f3(f4(f5(c12)), c13)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (p2(f6(c15, c11), f3(f4(f5(c12)), c13)) | (~p2(c16, f6(c15, c11))) | (~p2(c16, f3(f4(f5(c12)), c13)))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[127])).
% 0.20/0.39 tff(129,plain,
% 0.20/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c16, f3(f4(f5(c12)), c13))) | (~p2(c16, f6(c15, c11))) | p2(f6(c15, c11), f3(f4(f5(c12)), c13)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | p2(f6(c15, c11), f3(f4(f5(c12)), c13)) | (~p2(c16, f6(c15, c11))) | (~p2(c16, f3(f4(f5(c12)), c13))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[128, 126])).
% 0.20/0.39 tff(130,plain,
% 0.20/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c16, f3(f4(f5(c12)), c13))) | (~p2(c16, f6(c15, c11))) | p2(f6(c15, c11), f3(f4(f5(c12)), c13)))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(131,plain,
% 0.20/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | p2(f6(c15, c11), f3(f4(f5(c12)), c13)) | (~p2(c16, f6(c15, c11))) | (~p2(c16, f3(f4(f5(c12)), c13)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.20/0.39 tff(132,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[131, 56, 125, 105, 66])).
% 0.20/0.39 % SZS output end Proof
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------