%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN558-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:34 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN558-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 12:38:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(p6_type, type, (
% 0.20/0.39 p6: ( $i * $i ) > $o)).
% 0.20/0.39 tff(f3_type, type, (
% 0.20/0.39 f3: $i > $i)).
% 0.20/0.39 tff(c8_type, type, (
% 0.20/0.39 c8: $i)).
% 0.20/0.39 tff(c7_type, type, (
% 0.20/0.39 c7: $i)).
% 0.20/0.39 tff(p5_type, type, (
% 0.20/0.39 p5: ( $i * $i * $i ) > $o)).
% 0.20/0.39 tff(c10_type, type, (
% 0.20/0.39 c10: $i)).
% 0.20/0.39 tff(p2_type, type, (
% 0.20/0.39 p2: ( $i * $i ) > $o)).
% 0.20/0.39 tff(c9_type, type, (
% 0.20/0.39 c9: $i)).
% 0.20/0.39 tff(p4_type, type, (
% 0.20/0.39 p4: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,plain,
% 0.20/0.39 (^[X21: $i] : refl(p6(c7, f3(X21)) <=> p6(c7, f3(X21)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(2,plain,
% 0.20/0.39 (![X21: $i] : p6(c7, f3(X21)) <=> ![X21: $i] : p6(c7, f3(X21))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (![X21: $i] : p6(c7, f3(X21)) <=> ![X21: $i] : p6(c7, f3(X21))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(4,axiom,(![X21: $i] : p6(c7, f3(X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p6_3')).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![X21: $i] : p6(c7, f3(X21))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.39 tff(6,plain,(
% 0.20/0.39 ![X21: $i] : p6(c7, f3(X21))),
% 0.20/0.39 inference(skolemize,[status(sab)],[5])).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![X21: $i] : p6(c7, f3(X21))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.39 tff(8,plain,
% 0.20/0.39 ((~![X21: $i] : p6(c7, f3(X21))) | p6(c7, f3(c8))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (p6(c7, f3(c8))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 (^[X21: $i] : refl(p5(c7, X21, f3(X21)) <=> p5(c7, X21, f3(X21)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 (![X21: $i] : p5(c7, X21, f3(X21)) <=> ![X21: $i] : p5(c7, X21, f3(X21))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.39 tff(12,plain,
% 0.20/0.39 (![X21: $i] : p5(c7, X21, f3(X21)) <=> ![X21: $i] : p5(c7, X21, f3(X21))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(13,axiom,(![X21: $i] : p5(c7, X21, f3(X21))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_6')).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (![X21: $i] : p5(c7, X21, f3(X21))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.39 tff(15,plain,(
% 0.20/0.39 ![X21: $i] : p5(c7, X21, f3(X21))),
% 0.20/0.39 inference(skolemize,[status(sab)],[14])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (![X21: $i] : p5(c7, X21, f3(X21))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 ((~![X21: $i] : p5(c7, X21, f3(X21))) | p5(c7, c8, f3(c8))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(18,plain,
% 0.20/0.39 (p5(c7, c8, f3(c8))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (^[X14: $i, X12: $i, X11: $i, X13: $i] : refl(((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13)) <=> ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13)) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13)) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (^[X14: $i, X12: $i, X11: $i, X13: $i] : trans(monotonicity(rewrite((p5(X11, X12, X13) | (~p5(X11, X12, X14))) <=> ((~p5(X11, X12, X14)) | p5(X11, X12, X13))), (((p5(X11, X12, X13) | (~p5(X11, X12, X14))) | (~p5(X11, X14, X13))) <=> (((~p5(X11, X12, X14)) | p5(X11, X12, X13)) | (~p5(X11, X14, X13))))), rewrite((((~p5(X11, X12, X14)) | p5(X11, X12, X13)) | (~p5(X11, X14, X13))) <=> ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))), (((p5(X11, X12, X13) | (~p5(X11, X12, X14))) | (~p5(X11, X14, X13))) <=> ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((p5(X11, X12, X13) | (~p5(X11, X12, X14))) | (~p5(X11, X14, X13))) <=> ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.40 tff(24,axiom,(![X14: $i, X12: $i, X11: $i, X13: $i] : ((p5(X11, X12, X13) | (~p5(X11, X12, X14))) | (~p5(X11, X14, X13)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_11')).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.40 tff(27,plain,(
% 0.20/0.40 ![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))),
% 0.20/0.40 inference(skolemize,[status(sab)],[26])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (p5(c7, c10, c8) <=> p5(c7, c10, c8)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(30,axiom,(p5(c7, c10, c8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_5')).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (p5(c7, c10, c8)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | ((~p5(c7, c10, c8)) | p5(c7, c10, f3(c8)) | (~p5(c7, c8, f3(c8))))) <=> ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | (~p5(c7, c10, c8)) | p5(c7, c10, f3(c8)) | (~p5(c7, c8, f3(c8))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (((~p5(c7, c8, f3(c8))) | (~p5(c7, c10, c8)) | p5(c7, c10, f3(c8))) <=> ((~p5(c7, c10, c8)) | p5(c7, c10, f3(c8)) | (~p5(c7, c8, f3(c8))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | ((~p5(c7, c8, f3(c8))) | (~p5(c7, c10, c8)) | p5(c7, c10, f3(c8)))) <=> ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | ((~p5(c7, c10, c8)) | p5(c7, c10, f3(c8)) | (~p5(c7, c8, f3(c8)))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | ((~p5(c7, c8, f3(c8))) | (~p5(c7, c10, c8)) | p5(c7, c10, f3(c8)))) <=> ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | (~p5(c7, c10, c8)) | p5(c7, c10, f3(c8)) | (~p5(c7, c8, f3(c8))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[34, 32])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | ((~p5(c7, c8, f3(c8))) | (~p5(c7, c10, c8)) | p5(c7, c10, f3(c8)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | (~p5(c7, c10, c8)) | p5(c7, c10, f3(c8)) | (~p5(c7, c8, f3(c8)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (p5(c7, c10, f3(c8))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[37, 31, 28, 18])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (^[X0: $i] : refl(p2(X0, X0) <=> p2(X0, X0))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.20/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(42,axiom,(![X0: $i] : p2(X0, X0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_1')).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (![X0: $i] : p2(X0, X0)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.40 tff(44,plain,(
% 0.20/0.40 ![X0: $i] : p2(X0, X0)),
% 0.20/0.40 inference(skolemize,[status(sab)],[43])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (![X0: $i] : p2(X0, X0)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 ((~![X0: $i] : p2(X0, X0)) | p2(c8, c8)),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (p2(c8, c8)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.20/0.40 tff(48,assumption,(~p4(c7, c7)), introduced(assumption)).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (^[X8: $i] : refl(p4(X8, X8) <=> p4(X8, X8))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (![X8: $i] : p4(X8, X8) <=> ![X8: $i] : p4(X8, X8)),
% 0.20/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (![X8: $i] : p4(X8, X8) <=> ![X8: $i] : p4(X8, X8)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(52,axiom,(![X8: $i] : p4(X8, X8)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p4_2')).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (![X8: $i] : p4(X8, X8)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.40 tff(54,plain,(
% 0.20/0.40 ![X8: $i] : p4(X8, X8)),
% 0.20/0.40 inference(skolemize,[status(sab)],[53])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (![X8: $i] : p4(X8, X8)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 ((~![X8: $i] : p4(X8, X8)) | p4(c7, c7)),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[56, 55, 48])).
% 0.20/0.40 tff(58,plain,(p4(c7, c7)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 ((~![X21: $i] : p5(c7, X21, f3(X21))) | p5(c7, c9, f3(c9))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (p5(c7, c9, f3(c9))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[59, 16])).
% 0.20/0.40 tff(61,plain,
% 0.20/0.40 (^[X26: $i] : refl(((~p5(c7, c8, X26)) | (~p5(c7, c9, X26))) <=> ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![X26: $i] : ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26))) <=> ![X26: $i] : ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (![X26: $i] : ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26))) <=> ![X26: $i] : ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(64,axiom,(![X26: $i] : ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p5_8')).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (![X26: $i] : ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.40 tff(66,plain,(
% 0.20/0.40 ![X26: $i] : ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[65])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (![X26: $i] : ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (((~![X26: $i] : ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26)))) | ((~p5(c7, c8, f3(c9))) | (~p5(c7, c9, f3(c9))))) <=> ((~![X26: $i] : ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26)))) | (~p5(c7, c8, f3(c9))) | (~p5(c7, c9, f3(c9))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ((~![X26: $i] : ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26)))) | ((~p5(c7, c8, f3(c9))) | (~p5(c7, c9, f3(c9))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 ((~![X26: $i] : ((~p5(c7, c8, X26)) | (~p5(c7, c9, X26)))) | (~p5(c7, c8, f3(c9))) | (~p5(c7, c9, f3(c9)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (~p5(c7, c8, f3(c9))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[70, 67, 60])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (^[X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : refl(((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17)) <=> ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17)) <=> ![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[72])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17)) <=> ![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (^[X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p5(X15, X16, X17) | (~p2(X18, X16))) <=> ((~p2(X18, X16)) | p5(X15, X16, X17))), (((p5(X15, X16, X17) | (~p2(X18, X16))) | (~p2(X19, X17))) <=> (((~p2(X18, X16)) | p5(X15, X16, X17)) | (~p2(X19, X17))))), rewrite((((~p2(X18, X16)) | p5(X15, X16, X17)) | (~p2(X19, X17))) <=> ((~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))), (((p5(X15, X16, X17) | (~p2(X18, X16))) | (~p2(X19, X17))) <=> ((~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17)))), ((((p5(X15, X16, X17) | (~p2(X18, X16))) | (~p2(X19, X17))) | (~p4(X20, X15))) <=> (((~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17)) | (~p4(X20, X15))))), rewrite((((~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17)) | (~p4(X20, X15))) <=> ((~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))), ((((p5(X15, X16, X17) | (~p2(X18, X16))) | (~p2(X19, X17))) | (~p4(X20, X15))) <=> ((~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17)))), (((((p5(X15, X16, X17) | (~p2(X18, X16))) | (~p2(X19, X17))) | (~p4(X20, X15))) | (~p5(X20, X18, X19))) <=> (((~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17)) | (~p5(X20, X18, X19))))), rewrite((((~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17)) | (~p5(X20, X18, X19))) <=> ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))), (((((p5(X15, X16, X17) | (~p2(X18, X16))) | (~p2(X19, X17))) | (~p4(X20, X15))) | (~p5(X20, X18, X19))) <=> ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((((p5(X15, X16, X17) | (~p2(X18, X16))) | (~p2(X19, X17))) | (~p4(X20, X15))) | (~p5(X20, X18, X19))) <=> ![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.40 tff(77,axiom,(![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((((p5(X15, X16, X17) | (~p2(X18, X16))) | (~p2(X19, X17))) | (~p4(X20, X15))) | (~p5(X20, X18, X19)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_14')).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.40 tff(79,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.40 tff(80,plain,(
% 0.20/0.40 ![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))),
% 0.20/0.40 inference(skolemize,[status(sab)],[79])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.20/0.40 tff(82,plain,
% 0.20/0.40 (((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))) | (p5(c7, c8, f3(c9)) | (~p4(c7, c7)) | (~p2(c8, c8)) | (~p2(f3(c8), f3(c9))) | (~p5(c7, c8, f3(c8))))) <=> ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))) | p5(c7, c8, f3(c9)) | (~p4(c7, c7)) | (~p2(c8, c8)) | (~p2(f3(c8), f3(c9))) | (~p5(c7, c8, f3(c8))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 (((~p5(c7, c8, f3(c8))) | (~p4(c7, c7)) | (~p2(f3(c8), f3(c9))) | (~p2(c8, c8)) | p5(c7, c8, f3(c9))) <=> (p5(c7, c8, f3(c9)) | (~p4(c7, c7)) | (~p2(c8, c8)) | (~p2(f3(c8), f3(c9))) | (~p5(c7, c8, f3(c8))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))) | ((~p5(c7, c8, f3(c8))) | (~p4(c7, c7)) | (~p2(f3(c8), f3(c9))) | (~p2(c8, c8)) | p5(c7, c8, f3(c9)))) <=> ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))) | (p5(c7, c8, f3(c9)) | (~p4(c7, c7)) | (~p2(c8, c8)) | (~p2(f3(c8), f3(c9))) | (~p5(c7, c8, f3(c8)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[83])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))) | ((~p5(c7, c8, f3(c8))) | (~p4(c7, c7)) | (~p2(f3(c8), f3(c9))) | (~p2(c8, c8)) | p5(c7, c8, f3(c9)))) <=> ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))) | p5(c7, c8, f3(c9)) | (~p4(c7, c7)) | (~p2(c8, c8)) | (~p2(f3(c8), f3(c9))) | (~p5(c7, c8, f3(c8))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[84, 82])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))) | ((~p5(c7, c8, f3(c8))) | (~p4(c7, c7)) | (~p2(f3(c8), f3(c9))) | (~p2(c8, c8)) | p5(c7, c8, f3(c9)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 ((~![X17: $i, X16: $i, X18: $i, X20: $i, X15: $i, X19: $i] : ((~p5(X20, X18, X19)) | (~p4(X20, X15)) | (~p2(X19, X17)) | (~p2(X18, X16)) | p5(X15, X16, X17))) | p5(c7, c8, f3(c9)) | (~p4(c7, c7)) | (~p2(c8, c8)) | (~p2(f3(c8), f3(c9))) | (~p5(c7, c8, f3(c8)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (~p2(f3(c8), f3(c9))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[87, 81, 71, 58, 47, 18])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (p5(c7, c10, c9) <=> p5(c7, c10, c9)),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(90,axiom,(p5(c7, c10, c9)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_4')).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (p5(c7, c10, c9)),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | ((~p5(c7, c10, c9)) | p5(c7, c10, f3(c9)) | (~p5(c7, c9, f3(c9))))) <=> ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | (~p5(c7, c10, c9)) | p5(c7, c10, f3(c9)) | (~p5(c7, c9, f3(c9))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (((~p5(c7, c9, f3(c9))) | (~p5(c7, c10, c9)) | p5(c7, c10, f3(c9))) <=> ((~p5(c7, c10, c9)) | p5(c7, c10, f3(c9)) | (~p5(c7, c9, f3(c9))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | ((~p5(c7, c9, f3(c9))) | (~p5(c7, c10, c9)) | p5(c7, c10, f3(c9)))) <=> ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | ((~p5(c7, c10, c9)) | p5(c7, c10, f3(c9)) | (~p5(c7, c9, f3(c9)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[93])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | ((~p5(c7, c9, f3(c9))) | (~p5(c7, c10, c9)) | p5(c7, c10, f3(c9)))) <=> ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | (~p5(c7, c10, c9)) | p5(c7, c10, f3(c9)) | (~p5(c7, c9, f3(c9))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[94, 92])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | ((~p5(c7, c9, f3(c9))) | (~p5(c7, c10, c9)) | p5(c7, c10, f3(c9)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 ((~![X14: $i, X12: $i, X11: $i, X13: $i] : ((~p5(X11, X14, X13)) | (~p5(X11, X12, X14)) | p5(X11, X12, X13))) | (~p5(c7, c10, c9)) | p5(c7, c10, f3(c9)) | (~p5(c7, c9, f3(c9)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (p5(c7, c10, f3(c9))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[97, 91, 28, 60])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 ((~![X21: $i] : p6(c7, f3(X21))) | p6(c7, f3(c9))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 (p6(c7, f3(c9))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[99, 7])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (^[X4: $i, X3: $i, X5: $i] : refl(((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4)) <=> ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4)))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4)) <=> ![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4)) <=> ![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (^[X4: $i, X3: $i, X5: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p2(X3, X4) | (~p6(c7, X4))) <=> ((~p6(c7, X4)) | p2(X3, X4))), (((p2(X3, X4) | (~p6(c7, X4))) | (~p6(c7, X3))) <=> (((~p6(c7, X4)) | p2(X3, X4)) | (~p6(c7, X3))))), rewrite((((~p6(c7, X4)) | p2(X3, X4)) | (~p6(c7, X3))) <=> ((~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))), (((p2(X3, X4) | (~p6(c7, X4))) | (~p6(c7, X3))) <=> ((~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4)))), ((((p2(X3, X4) | (~p6(c7, X4))) | (~p6(c7, X3))) | (~p5(c7, X5, X4))) <=> (((~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4)) | (~p5(c7, X5, X4))))), rewrite((((~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4)) | (~p5(c7, X5, X4))) <=> ((~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))), ((((p2(X3, X4) | (~p6(c7, X4))) | (~p6(c7, X3))) | (~p5(c7, X5, X4))) <=> ((~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4)))), (((((p2(X3, X4) | (~p6(c7, X4))) | (~p6(c7, X3))) | (~p5(c7, X5, X4))) | (~p5(c7, X5, X3))) <=> (((~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4)) | (~p5(c7, X5, X3))))), rewrite((((~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4)) | (~p5(c7, X5, X3))) <=> ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))), (((((p2(X3, X4) | (~p6(c7, X4))) | (~p6(c7, X3))) | (~p5(c7, X5, X4))) | (~p5(c7, X5, X3))) <=> ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (![X4: $i, X3: $i, X5: $i] : ((((p2(X3, X4) | (~p6(c7, X4))) | (~p6(c7, X3))) | (~p5(c7, X5, X4))) | (~p5(c7, X5, X3))) <=> ![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.41 tff(106,axiom,(![X4: $i, X3: $i, X5: $i] : ((((p2(X3, X4) | (~p6(c7, X4))) | (~p6(c7, X3))) | (~p5(c7, X5, X4))) | (~p5(c7, X5, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_13')).
% 0.20/0.41 tff(107,plain,
% 0.20/0.41 (![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 (![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.20/0.41 tff(109,plain,(
% 0.20/0.41 ![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))),
% 0.20/0.41 inference(skolemize,[status(sab)],[108])).
% 0.20/0.41 tff(110,plain,
% 0.20/0.41 (![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (((~![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))) | ((~p5(c7, c10, f3(c9))) | (~p6(c7, f3(c9))) | (~p5(c7, c10, f3(c8))) | (~p6(c7, f3(c8))) | p2(f3(c8), f3(c9)))) <=> ((~![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))) | (~p5(c7, c10, f3(c9))) | (~p6(c7, f3(c9))) | (~p5(c7, c10, f3(c8))) | (~p6(c7, f3(c8))) | p2(f3(c8), f3(c9)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (((~p5(c7, c10, f3(c8))) | (~p5(c7, c10, f3(c9))) | (~p6(c7, f3(c8))) | (~p6(c7, f3(c9))) | p2(f3(c8), f3(c9))) <=> ((~p5(c7, c10, f3(c9))) | (~p6(c7, f3(c9))) | (~p5(c7, c10, f3(c8))) | (~p6(c7, f3(c8))) | p2(f3(c8), f3(c9)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (((~![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))) | ((~p5(c7, c10, f3(c8))) | (~p5(c7, c10, f3(c9))) | (~p6(c7, f3(c8))) | (~p6(c7, f3(c9))) | p2(f3(c8), f3(c9)))) <=> ((~![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))) | ((~p5(c7, c10, f3(c9))) | (~p6(c7, f3(c9))) | (~p5(c7, c10, f3(c8))) | (~p6(c7, f3(c8))) | p2(f3(c8), f3(c9))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (((~![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))) | ((~p5(c7, c10, f3(c8))) | (~p5(c7, c10, f3(c9))) | (~p6(c7, f3(c8))) | (~p6(c7, f3(c9))) | p2(f3(c8), f3(c9)))) <=> ((~![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))) | (~p5(c7, c10, f3(c9))) | (~p6(c7, f3(c9))) | (~p5(c7, c10, f3(c8))) | (~p6(c7, f3(c8))) | p2(f3(c8), f3(c9)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[113, 111])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((~![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))) | ((~p5(c7, c10, f3(c8))) | (~p5(c7, c10, f3(c9))) | (~p6(c7, f3(c8))) | (~p6(c7, f3(c9))) | p2(f3(c8), f3(c9)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 ((~![X4: $i, X3: $i, X5: $i] : ((~p5(c7, X5, X3)) | (~p5(c7, X5, X4)) | (~p6(c7, X3)) | (~p6(c7, X4)) | p2(X3, X4))) | (~p5(c7, c10, f3(c9))) | (~p6(c7, f3(c9))) | (~p5(c7, c10, f3(c8))) | (~p6(c7, f3(c8))) | p2(f3(c8), f3(c9))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[116, 110, 100, 98, 88, 38, 9])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------