%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN577-1 : 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 05:39:36 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN577-1 : TPTP v9.0.0. Released v2.5.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 12:40:27 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(p2_type, type, (
% 0.18/0.37 p2: ( $i * $i ) > $o)).
% 0.18/0.37 tff(f5_type, type, (
% 0.18/0.37 f5: ( $i * $i ) > $i)).
% 0.18/0.37 tff(c19_type, type, (
% 0.18/0.37 c19: $i)).
% 0.18/0.37 tff(f6_type, type, (
% 0.18/0.37 f6: $i > $i)).
% 0.18/0.37 tff(c9_type, type, (
% 0.18/0.37 c9: $i)).
% 0.18/0.37 tff(f4_type, type, (
% 0.18/0.37 f4: ( $i * $i ) > $i)).
% 0.18/0.37 tff(c14_type, type, (
% 0.18/0.37 c14: $i)).
% 0.18/0.37 tff(c15_type, type, (
% 0.18/0.37 c15: $i)).
% 0.18/0.37 tff(c17_type, type, (
% 0.18/0.37 c17: $i)).
% 0.18/0.37 tff(f3_type, type, (
% 0.18/0.37 f3: ( $i * $i ) > $i)).
% 0.18/0.37 tff(c11_type, type, (
% 0.18/0.37 c11: $i)).
% 0.18/0.37 tff(c12_type, type, (
% 0.18/0.37 c12: $i)).
% 0.18/0.37 tff(c20_type, type, (
% 0.18/0.37 c20: $i)).
% 0.18/0.37 tff(c16_type, type, (
% 0.18/0.37 c16: $i)).
% 0.18/0.37 tff(c18_type, type, (
% 0.18/0.37 c18: $i)).
% 0.18/0.37 tff(c13_type, type, (
% 0.18/0.37 c13: $i)).
% 0.18/0.37 tff(p7_type, type, (
% 0.18/0.37 p7: ( $i * $i ) > $o)).
% 0.18/0.37 tff(c10_type, type, (
% 0.18/0.37 c10: $i)).
% 0.18/0.37 tff(1,assumption,(~p2(c19, c19)), introduced(assumption)).
% 0.18/0.37 tff(2,plain,
% 0.18/0.37 (^[X0: $i] : refl(p2(X0, X0) <=> p2(X0, X0))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.18/0.37 inference(quant_intro,[status(thm)],[2])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![X0: $i] : p2(X0, X0) <=> ![X0: $i] : p2(X0, X0)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(5,axiom,(![X0: $i] : p2(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_1')).
% 0.18/0.37 tff(6,plain,
% 0.18/0.37 (![X0: $i] : p2(X0, X0)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.18/0.37 tff(7,plain,(
% 0.18/0.37 ![X0: $i] : p2(X0, X0)),
% 0.18/0.37 inference(skolemize,[status(sab)],[6])).
% 0.18/0.37 tff(8,plain,
% 0.18/0.37 (![X0: $i] : p2(X0, X0)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 ((~![X0: $i] : p2(X0, X0)) | p2(c19, c19)),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.18/0.37 tff(11,plain,(p2(c19, c19)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(12,assumption,(~p2(f6(c9), f6(c9))), introduced(assumption)).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 ((~![X0: $i] : p2(X0, X0)) | p2(f6(c9), f6(c9))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[13, 8, 12])).
% 0.18/0.37 tff(15,plain,(p2(f6(c9), f6(c9))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (^[X21: $i, X18: $i, X20: $i, X19: $i] : refl(((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21))) <=> ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21))) <=> ![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 (![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21))) <=> ![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (^[X21: $i, X18: $i, X20: $i, X19: $i] : trans(monotonicity(rewrite((p2(f5(X18, X19), f5(X20, X21)) | (~p2(X19, X21))) <=> ((~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))), (((p2(f5(X18, X19), f5(X20, X21)) | (~p2(X19, X21))) | (~p2(X18, X20))) <=> (((~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21))) | (~p2(X18, X20))))), rewrite((((~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21))) | (~p2(X18, X20))) <=> ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))), (((p2(f5(X18, X19), f5(X20, X21)) | (~p2(X19, X21))) | (~p2(X18, X20))) <=> ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (![X21: $i, X18: $i, X20: $i, X19: $i] : ((p2(f5(X18, X19), f5(X20, X21)) | (~p2(X19, X21))) | (~p2(X18, X20))) <=> ![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[19])).
% 0.18/0.37 tff(21,axiom,(![X21: $i, X18: $i, X20: $i, X19: $i] : ((p2(f5(X18, X19), f5(X20, X21)) | (~p2(X19, X21))) | (~p2(X18, X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_18')).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.18/0.37 tff(24,plain,(
% 0.18/0.37 ![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[23])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 (((~![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))) | ((~p2(f6(c9), f6(c9))) | (~p2(c19, c19)) | p2(f5(f6(c9), c19), f5(f6(c9), c19)))) <=> ((~![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))) | (~p2(f6(c9), f6(c9))) | (~p2(c19, c19)) | p2(f5(f6(c9), c19), f5(f6(c9), c19)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 ((~![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))) | ((~p2(f6(c9), f6(c9))) | (~p2(c19, c19)) | p2(f5(f6(c9), c19), f5(f6(c9), c19)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 ((~![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))) | (~p2(f6(c9), f6(c9))) | (~p2(c19, c19)) | p2(f5(f6(c9), c19), f5(f6(c9), c19))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 ((~p2(f6(c9), f6(c9))) | (~p2(c19, c19)) | p2(f5(f6(c9), c19), f5(f6(c9), c19))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 ((~p2(c19, c19)) | p2(f5(f6(c9), c19), f5(f6(c9), c19))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[29, 15])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (p2(f5(f6(c9), c19), f5(f6(c9), c19))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[30, 11])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (^[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)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (![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))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[32])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (![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))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 (^[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))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (![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))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[35])).
% 0.18/0.37 tff(37,axiom,(![X0: $i, X2: $i, X1: $i] : ((p2(X1, X2) | (~p2(X0, X1))) | (~p2(X0, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_14')).
% 0.18/0.37 tff(38,plain,
% 0.18/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.18/0.37 tff(40,plain,(
% 0.18/0.37 ![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.18/0.37 inference(skolemize,[status(sab)],[39])).
% 0.18/0.37 tff(41,plain,
% 0.18/0.37 (![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.18/0.37 tff(42,plain,
% 0.18/0.37 (p2(f5(f6(c9), c19), c17) <=> p2(f5(f6(c9), c19), c17)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(43,axiom,(p2(f5(f6(c9), c19), c17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_11')).
% 0.18/0.37 tff(44,plain,
% 0.18/0.37 (p2(f5(f6(c9), c19), c17)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.18/0.37 tff(45,plain,
% 0.18/0.37 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f5(f6(c9), c19), f5(f6(c9), c19))) | (~p2(f5(f6(c9), c19), c17)) | p2(c17, f5(f6(c9), c19)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f5(f6(c9), c19), f5(f6(c9), c19))) | (~p2(f5(f6(c9), c19), c17)) | p2(c17, f5(f6(c9), c19)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f5(f6(c9), c19), f5(f6(c9), c19))) | (~p2(f5(f6(c9), c19), c17)) | p2(c17, f5(f6(c9), c19)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f5(f6(c9), c19), f5(f6(c9), c19))) | (~p2(f5(f6(c9), c19), c17)) | p2(c17, f5(f6(c9), c19))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 (p2(c17, f5(f6(c9), c19))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[47, 44, 41, 31])).
% 0.18/0.37 tff(49,assumption,(~p2(c14, c14)), introduced(assumption)).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 ((~![X0: $i] : p2(X0, X0)) | p2(c14, c14)),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[50, 8, 49])).
% 0.18/0.37 tff(52,plain,(p2(c14, c14)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(53,plain,
% 0.18/0.37 (p2(f3(c12, c11), c15) <=> p2(f3(c12, c11), c15)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(54,axiom,(p2(f3(c12, c11), c15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_7')).
% 0.18/0.37 tff(55,plain,
% 0.18/0.37 (p2(f3(c12, c11), c15)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.18/0.37 tff(56,plain,
% 0.18/0.37 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(c12, c11), c15)) | p2(c15, c15))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f3(c12, c11), c15)) | p2(c15, c15))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(57,plain,
% 0.18/0.37 (((~p2(f3(c12, c11), c15)) | (~p2(f3(c12, c11), c15)) | p2(c15, c15)) <=> ((~p2(f3(c12, c11), c15)) | p2(c15, c15))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(c12, c11), c15)) | (~p2(f3(c12, c11), c15)) | p2(c15, c15))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(c12, c11), c15)) | p2(c15, c15)))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[57])).
% 0.18/0.37 tff(59,plain,
% 0.18/0.37 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(c12, c11), c15)) | (~p2(f3(c12, c11), c15)) | p2(c15, c15))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f3(c12, c11), c15)) | p2(c15, c15))),
% 0.18/0.37 inference(transitivity,[status(thm)],[58, 56])).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(c12, c11), c15)) | (~p2(f3(c12, c11), c15)) | p2(c15, c15))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(61,plain,
% 0.18/0.37 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f3(c12, c11), c15)) | p2(c15, c15)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.18/0.37 tff(62,plain,
% 0.18/0.37 (p2(c15, c15)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[61, 55, 41])).
% 0.18/0.37 tff(63,plain,
% 0.18/0.37 (^[X14: $i, X17: $i, X16: $i, X15: $i] : refl(((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17))) <=> ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(64,plain,
% 0.18/0.37 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17))) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[63])).
% 0.18/0.38 tff(65,plain,
% 0.18/0.38 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17))) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(66,plain,
% 0.18/0.38 (^[X14: $i, X17: $i, X16: $i, X15: $i] : trans(monotonicity(rewrite((p2(f4(X14, X15), f4(X16, X17)) | (~p2(X14, X16))) <=> ((~p2(X14, X16)) | p2(f4(X14, X15), f4(X16, X17)))), (((p2(f4(X14, X15), f4(X16, X17)) | (~p2(X14, X16))) | (~p2(X15, X17))) <=> (((~p2(X14, X16)) | p2(f4(X14, X15), f4(X16, X17))) | (~p2(X15, X17))))), rewrite((((~p2(X14, X16)) | p2(f4(X14, X15), f4(X16, X17))) | (~p2(X15, X17))) <=> ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))), (((p2(f4(X14, X15), f4(X16, X17)) | (~p2(X14, X16))) | (~p2(X15, X17))) <=> ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(67,plain,
% 0.18/0.38 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((p2(f4(X14, X15), f4(X16, X17)) | (~p2(X14, X16))) | (~p2(X15, X17))) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[66])).
% 0.18/0.38 tff(68,axiom,(![X14: $i, X17: $i, X16: $i, X15: $i] : ((p2(f4(X14, X15), f4(X16, X17)) | (~p2(X14, X16))) | (~p2(X15, X17)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_19')).
% 0.18/0.38 tff(69,plain,
% 0.18/0.38 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.18/0.38 tff(70,plain,
% 0.18/0.38 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.18/0.38 tff(71,plain,(
% 0.18/0.38 ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[70])).
% 0.18/0.38 tff(72,plain,
% 0.18/0.38 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[71, 64])).
% 0.18/0.38 tff(73,plain,
% 0.18/0.38 (((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))) | ((~p2(c14, c14)) | (~p2(c15, c15)) | p2(f4(c15, c14), f4(c15, c14)))) <=> ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))) | (~p2(c14, c14)) | (~p2(c15, c15)) | p2(f4(c15, c14), f4(c15, c14)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(74,plain,
% 0.18/0.38 (((~p2(c15, c15)) | (~p2(c14, c14)) | p2(f4(c15, c14), f4(c15, c14))) <=> ((~p2(c14, c14)) | (~p2(c15, c15)) | p2(f4(c15, c14), f4(c15, c14)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(75,plain,
% 0.18/0.38 (((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))) | ((~p2(c15, c15)) | (~p2(c14, c14)) | p2(f4(c15, c14), f4(c15, c14)))) <=> ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))) | ((~p2(c14, c14)) | (~p2(c15, c15)) | p2(f4(c15, c14), f4(c15, c14))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[74])).
% 0.18/0.38 tff(76,plain,
% 0.18/0.38 (((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))) | ((~p2(c15, c15)) | (~p2(c14, c14)) | p2(f4(c15, c14), f4(c15, c14)))) <=> ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))) | (~p2(c14, c14)) | (~p2(c15, c15)) | p2(f4(c15, c14), f4(c15, c14)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[75, 73])).
% 0.18/0.38 tff(77,plain,
% 0.18/0.38 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))) | ((~p2(c15, c15)) | (~p2(c14, c14)) | p2(f4(c15, c14), f4(c15, c14)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(78,plain,
% 0.18/0.38 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))) | (~p2(c14, c14)) | (~p2(c15, c15)) | p2(f4(c15, c14), f4(c15, c14))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.18/0.38 tff(79,plain,
% 0.18/0.38 ((~p2(c14, c14)) | p2(f4(c15, c14), f4(c15, c14))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[78, 72, 62])).
% 0.18/0.38 tff(80,plain,
% 0.18/0.38 (p2(f4(c15, c14), f4(c15, c14))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[79, 52])).
% 0.18/0.38 tff(81,plain,
% 0.18/0.38 (p2(f4(c15, c14), c17) <=> p2(f4(c15, c14), c17)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(82,axiom,(p2(f4(c15, c14), c17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_9')).
% 0.18/0.38 tff(83,plain,
% 0.18/0.38 (p2(f4(c15, c14), c17)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.18/0.38 tff(84,plain,
% 0.18/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f4(c15, c14), c17)) | (~p2(f4(c15, c14), f4(c15, c14))) | p2(c17, f4(c15, c14)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f4(c15, c14), c17)) | (~p2(f4(c15, c14), f4(c15, c14))) | p2(c17, f4(c15, c14)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(85,plain,
% 0.18/0.38 (((~p2(f4(c15, c14), f4(c15, c14))) | (~p2(f4(c15, c14), c17)) | p2(c17, f4(c15, c14))) <=> ((~p2(f4(c15, c14), c17)) | (~p2(f4(c15, c14), f4(c15, c14))) | p2(c17, f4(c15, c14)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(86,plain,
% 0.18/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f4(c15, c14), f4(c15, c14))) | (~p2(f4(c15, c14), c17)) | p2(c17, f4(c15, c14)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f4(c15, c14), c17)) | (~p2(f4(c15, c14), f4(c15, c14))) | p2(c17, f4(c15, c14))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[85])).
% 0.18/0.38 tff(87,plain,
% 0.18/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f4(c15, c14), f4(c15, c14))) | (~p2(f4(c15, c14), c17)) | p2(c17, f4(c15, c14)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f4(c15, c14), c17)) | (~p2(f4(c15, c14), f4(c15, c14))) | p2(c17, f4(c15, c14)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[86, 84])).
% 0.18/0.38 tff(88,plain,
% 0.18/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f4(c15, c14), f4(c15, c14))) | (~p2(f4(c15, c14), c17)) | p2(c17, f4(c15, c14)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(89,plain,
% 0.18/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f4(c15, c14), c17)) | (~p2(f4(c15, c14), f4(c15, c14))) | p2(c17, f4(c15, c14))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.38 tff(90,plain,
% 0.18/0.38 (p2(c17, f4(c15, c14))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[89, 83, 41, 80])).
% 0.18/0.38 tff(91,plain,
% 0.18/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c17, f4(c15, c14))) | (~p2(c17, f5(f6(c9), c19))) | p2(f4(c15, c14), f5(f6(c9), c19)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(c17, f4(c15, c14))) | (~p2(c17, f5(f6(c9), c19))) | p2(f4(c15, c14), f5(f6(c9), c19)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(92,plain,
% 0.18/0.38 (((~p2(c17, f5(f6(c9), c19))) | (~p2(c17, f4(c15, c14))) | p2(f4(c15, c14), f5(f6(c9), c19))) <=> ((~p2(c17, f4(c15, c14))) | (~p2(c17, f5(f6(c9), c19))) | p2(f4(c15, c14), f5(f6(c9), c19)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(93,plain,
% 0.18/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c17, f5(f6(c9), c19))) | (~p2(c17, f4(c15, c14))) | p2(f4(c15, c14), f5(f6(c9), c19)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c17, f4(c15, c14))) | (~p2(c17, f5(f6(c9), c19))) | p2(f4(c15, c14), f5(f6(c9), c19))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[92])).
% 0.18/0.38 tff(94,plain,
% 0.18/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c17, f5(f6(c9), c19))) | (~p2(c17, f4(c15, c14))) | p2(f4(c15, c14), f5(f6(c9), c19)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(c17, f4(c15, c14))) | (~p2(c17, f5(f6(c9), c19))) | p2(f4(c15, c14), f5(f6(c9), c19)))),
% 0.18/0.39 inference(transitivity,[status(thm)],[93, 91])).
% 0.18/0.39 tff(95,plain,
% 0.18/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c17, f5(f6(c9), c19))) | (~p2(c17, f4(c15, c14))) | p2(f4(c15, c14), f5(f6(c9), c19)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(96,plain,
% 0.18/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(c17, f4(c15, c14))) | (~p2(c17, f5(f6(c9), c19))) | p2(f4(c15, c14), f5(f6(c9), c19))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.18/0.39 tff(97,plain,
% 0.18/0.39 (p2(f4(c15, c14), f5(f6(c9), c19))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[96, 41, 90, 48])).
% 0.18/0.39 tff(98,assumption,(~p2(c20, c20)), introduced(assumption)).
% 0.18/0.39 tff(99,plain,
% 0.18/0.39 ((~![X0: $i] : p2(X0, X0)) | p2(c20, c20)),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(100,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[99, 8, 98])).
% 0.18/0.39 tff(101,plain,(p2(c20, c20)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(102,plain,
% 0.18/0.39 (((~![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))) | ((~p2(f6(c9), f6(c9))) | (~p2(c20, c20)) | p2(f5(f6(c9), c20), f5(f6(c9), c20)))) <=> ((~![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))) | (~p2(f6(c9), f6(c9))) | (~p2(c20, c20)) | p2(f5(f6(c9), c20), f5(f6(c9), c20)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(103,plain,
% 0.18/0.39 ((~![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))) | ((~p2(f6(c9), f6(c9))) | (~p2(c20, c20)) | p2(f5(f6(c9), c20), f5(f6(c9), c20)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(104,plain,
% 0.18/0.39 ((~![X21: $i, X18: $i, X20: $i, X19: $i] : ((~p2(X18, X20)) | (~p2(X19, X21)) | p2(f5(X18, X19), f5(X20, X21)))) | (~p2(f6(c9), f6(c9))) | (~p2(c20, c20)) | p2(f5(f6(c9), c20), f5(f6(c9), c20))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.18/0.39 tff(105,plain,
% 0.18/0.39 ((~p2(f6(c9), f6(c9))) | (~p2(c20, c20)) | p2(f5(f6(c9), c20), f5(f6(c9), c20))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[104, 25])).
% 0.18/0.39 tff(106,plain,
% 0.18/0.39 ((~p2(c20, c20)) | p2(f5(f6(c9), c20), f5(f6(c9), c20))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[105, 15])).
% 0.18/0.39 tff(107,plain,
% 0.18/0.39 (p2(f5(f6(c9), c20), f5(f6(c9), c20))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[106, 101])).
% 0.18/0.39 tff(108,plain,
% 0.18/0.39 (p2(f5(f6(c9), c20), c18) <=> p2(f5(f6(c9), c20), c18)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(109,axiom,(p2(f5(f6(c9), c20), c18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_12')).
% 0.18/0.39 tff(110,plain,
% 0.18/0.39 (p2(f5(f6(c9), c20), c18)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.18/0.39 tff(111,plain,
% 0.18/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f5(f6(c9), c20), f5(f6(c9), c20))) | (~p2(f5(f6(c9), c20), c18)) | p2(c18, f5(f6(c9), c20)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f5(f6(c9), c20), f5(f6(c9), c20))) | (~p2(f5(f6(c9), c20), c18)) | p2(c18, f5(f6(c9), c20)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(112,plain,
% 0.18/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f5(f6(c9), c20), f5(f6(c9), c20))) | (~p2(f5(f6(c9), c20), c18)) | p2(c18, f5(f6(c9), c20)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(113,plain,
% 0.18/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f5(f6(c9), c20), f5(f6(c9), c20))) | (~p2(f5(f6(c9), c20), c18)) | p2(c18, f5(f6(c9), c20))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.18/0.39 tff(114,plain,
% 0.18/0.39 (p2(c18, f5(f6(c9), c20))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[113, 110, 41, 107])).
% 0.18/0.39 tff(115,plain,
% 0.18/0.39 (p2(f3(c12, c13), c16) <=> p2(f3(c12, c13), c16)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(116,axiom,(p2(f3(c12, c13), c16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_10')).
% 0.18/0.39 tff(117,plain,
% 0.18/0.39 (p2(f3(c12, c13), c16)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.18/0.39 tff(118,plain,
% 0.18/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(c12, c13), c16)) | p2(c16, c16))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f3(c12, c13), c16)) | p2(c16, c16))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(119,plain,
% 0.18/0.39 (((~p2(f3(c12, c13), c16)) | (~p2(f3(c12, c13), c16)) | p2(c16, c16)) <=> ((~p2(f3(c12, c13), c16)) | p2(c16, c16))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(120,plain,
% 0.18/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(c12, c13), c16)) | (~p2(f3(c12, c13), c16)) | p2(c16, c16))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(c12, c13), c16)) | p2(c16, c16)))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[119])).
% 0.18/0.39 tff(121,plain,
% 0.18/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(c12, c13), c16)) | (~p2(f3(c12, c13), c16)) | p2(c16, c16))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f3(c12, c13), c16)) | p2(c16, c16))),
% 0.18/0.39 inference(transitivity,[status(thm)],[120, 118])).
% 0.18/0.39 tff(122,plain,
% 0.18/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f3(c12, c13), c16)) | (~p2(f3(c12, c13), c16)) | p2(c16, c16))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(123,plain,
% 0.18/0.39 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f3(c12, c13), c16)) | p2(c16, c16)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.18/0.39 tff(124,plain,
% 0.18/0.39 (p2(c16, c16)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[123, 117, 41])).
% 0.18/0.39 tff(125,plain,
% 0.18/0.39 (((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))) | ((~p2(c16, c16)) | (~p2(c14, c14)) | p2(f4(c16, c14), f4(c16, c14)))) <=> ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))) | (~p2(c16, c16)) | (~p2(c14, c14)) | p2(f4(c16, c14), f4(c16, c14)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(126,plain,
% 0.18/0.39 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))) | ((~p2(c16, c16)) | (~p2(c14, c14)) | p2(f4(c16, c14), f4(c16, c14)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(127,plain,
% 0.18/0.39 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X14, X16)) | (~p2(X15, X17)) | p2(f4(X14, X15), f4(X16, X17)))) | (~p2(c16, c16)) | (~p2(c14, c14)) | p2(f4(c16, c14), f4(c16, c14))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.18/0.39 tff(128,plain,
% 0.18/0.39 ((~p2(c14, c14)) | p2(f4(c16, c14), f4(c16, c14))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[127, 72, 124])).
% 0.18/0.39 tff(129,plain,
% 0.18/0.39 (p2(f4(c16, c14), f4(c16, c14))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[128, 52])).
% 0.18/0.39 tff(130,plain,
% 0.18/0.39 (p2(f4(c16, c14), c18) <=> p2(f4(c16, c14), c18)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(131,axiom,(p2(f4(c16, c14), c18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_8')).
% 0.18/0.39 tff(132,plain,
% 0.18/0.39 (p2(f4(c16, c14), c18)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.18/0.39 tff(133,plain,
% 0.18/0.39 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f4(c16, c14), c18)) | (~p2(f4(c16, c14), f4(c16, c14))) | p2(c18, f4(c16, c14)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f4(c16, c14), c18)) | (~p2(f4(c16, c14), f4(c16, c14))) | p2(c18, f4(c16, c14)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(134,plain,
% 0.18/0.39 (((~p2(f4(c16, c14), f4(c16, c14))) | (~p2(f4(c16, c14), c18)) | p2(c18, f4(c16, c14))) <=> ((~p2(f4(c16, c14), c18)) | (~p2(f4(c16, c14), f4(c16, c14))) | p2(c18, f4(c16, c14)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(135,plain,
% 0.18/0.40 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f4(c16, c14), f4(c16, c14))) | (~p2(f4(c16, c14), c18)) | p2(c18, f4(c16, c14)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f4(c16, c14), c18)) | (~p2(f4(c16, c14), f4(c16, c14))) | p2(c18, f4(c16, c14))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[134])).
% 0.18/0.40 tff(136,plain,
% 0.18/0.40 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f4(c16, c14), f4(c16, c14))) | (~p2(f4(c16, c14), c18)) | p2(c18, f4(c16, c14)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f4(c16, c14), c18)) | (~p2(f4(c16, c14), f4(c16, c14))) | p2(c18, f4(c16, c14)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[135, 133])).
% 0.18/0.40 tff(137,plain,
% 0.18/0.40 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(f4(c16, c14), f4(c16, c14))) | (~p2(f4(c16, c14), c18)) | p2(c18, f4(c16, c14)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(138,plain,
% 0.18/0.40 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(f4(c16, c14), c18)) | (~p2(f4(c16, c14), f4(c16, c14))) | p2(c18, f4(c16, c14))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.18/0.40 tff(139,plain,
% 0.18/0.40 (p2(c18, f4(c16, c14))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[138, 132, 41, 129])).
% 0.18/0.40 tff(140,plain,
% 0.18/0.40 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c18, f4(c16, c14))) | (~p2(c18, f5(f6(c9), c20))) | p2(f4(c16, c14), f5(f6(c9), c20)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(c18, f4(c16, c14))) | (~p2(c18, f5(f6(c9), c20))) | p2(f4(c16, c14), f5(f6(c9), c20)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(141,plain,
% 0.18/0.40 (((~p2(c18, f5(f6(c9), c20))) | (~p2(c18, f4(c16, c14))) | p2(f4(c16, c14), f5(f6(c9), c20))) <=> ((~p2(c18, f4(c16, c14))) | (~p2(c18, f5(f6(c9), c20))) | p2(f4(c16, c14), f5(f6(c9), c20)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(142,plain,
% 0.18/0.40 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c18, f5(f6(c9), c20))) | (~p2(c18, f4(c16, c14))) | p2(f4(c16, c14), f5(f6(c9), c20)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c18, f4(c16, c14))) | (~p2(c18, f5(f6(c9), c20))) | p2(f4(c16, c14), f5(f6(c9), c20))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[141])).
% 0.18/0.40 tff(143,plain,
% 0.18/0.40 (((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c18, f5(f6(c9), c20))) | (~p2(c18, f4(c16, c14))) | p2(f4(c16, c14), f5(f6(c9), c20)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(c18, f4(c16, c14))) | (~p2(c18, f5(f6(c9), c20))) | p2(f4(c16, c14), f5(f6(c9), c20)))),
% 0.18/0.40 inference(transitivity,[status(thm)],[142, 140])).
% 0.18/0.40 tff(144,plain,
% 0.18/0.40 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | ((~p2(c18, f5(f6(c9), c20))) | (~p2(c18, f4(c16, c14))) | p2(f4(c16, c14), f5(f6(c9), c20)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(145,plain,
% 0.18/0.40 ((~![X0: $i, X2: $i, X1: $i] : ((~p2(X0, X2)) | (~p2(X0, X1)) | p2(X1, X2))) | (~p2(c18, f4(c16, c14))) | (~p2(c18, f5(f6(c9), c20))) | p2(f4(c16, c14), f5(f6(c9), c20))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.18/0.40 tff(146,plain,
% 0.18/0.40 (p2(f4(c16, c14), f5(f6(c9), c20))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[145, 41, 139, 114])).
% 0.18/0.40 tff(147,plain,
% 0.18/0.40 (^[X32: $i, X34: $i, X33: $i] : refl(((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10))) <=> ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(148,plain,
% 0.18/0.40 (![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10))) <=> ![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[147])).
% 0.18/0.40 tff(149,plain,
% 0.18/0.40 (![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10))) <=> ![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(150,plain,
% 0.18/0.40 (^[X32: $i, X34: $i, X33: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~p7(X34, c10)) | (~p2(c15, X32))) <=> ((~p2(c15, X32)) | (~p7(X34, c10)))), ((((~p7(X34, c10)) | (~p2(c15, X32))) | (~p2(c16, X33))) <=> (((~p2(c15, X32)) | (~p7(X34, c10))) | (~p2(c16, X33))))), rewrite((((~p2(c15, X32)) | (~p7(X34, c10))) | (~p2(c16, X33))) <=> ((~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))), ((((~p7(X34, c10)) | (~p2(c15, X32))) | (~p2(c16, X33))) <=> ((~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10))))), (((((~p7(X34, c10)) | (~p2(c15, X32))) | (~p2(c16, X33))) | (~p2(f4(X32, c14), f5(f6(X34), c19)))) <=> (((~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10))) | (~p2(f4(X32, c14), f5(f6(X34), c19)))))), rewrite((((~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10))) | (~p2(f4(X32, c14), f5(f6(X34), c19)))) <=> ((~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))), (((((~p7(X34, c10)) | (~p2(c15, X32))) | (~p2(c16, X33))) | (~p2(f4(X32, c14), f5(f6(X34), c19)))) <=> ((~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10))))), ((((((~p7(X34, c10)) | (~p2(c15, X32))) | (~p2(c16, X33))) | (~p2(f4(X32, c14), f5(f6(X34), c19)))) | (~p2(f4(X33, c14), f5(f6(X34), c20)))) <=> (((~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10))) | (~p2(f4(X33, c14), f5(f6(X34), c20)))))), rewrite((((~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10))) | (~p2(f4(X33, c14), f5(f6(X34), c20)))) <=> ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))), ((((((~p7(X34, c10)) | (~p2(c15, X32))) | (~p2(c16, X33))) | (~p2(f4(X32, c14), f5(f6(X34), c19)))) | (~p2(f4(X33, c14), f5(f6(X34), c20)))) <=> ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(151,plain,
% 0.18/0.40 (![X32: $i, X34: $i, X33: $i] : (((((~p7(X34, c10)) | (~p2(c15, X32))) | (~p2(c16, X33))) | (~p2(f4(X32, c14), f5(f6(X34), c19)))) | (~p2(f4(X33, c14), f5(f6(X34), c20)))) <=> ![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[150])).
% 0.18/0.40 tff(152,axiom,(![X32: $i, X34: $i, X33: $i] : (((((~p7(X34, c10)) | (~p2(c15, X32))) | (~p2(c16, X33))) | (~p2(f4(X32, c14), f5(f6(X34), c19)))) | (~p2(f4(X33, c14), f5(f6(X34), c20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p7_20')).
% 0.18/0.40 tff(153,plain,
% 0.18/0.40 (![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.18/0.40 tff(154,plain,
% 0.18/0.40 (![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.18/0.40 tff(155,plain,(
% 0.18/0.40 ![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[154])).
% 0.18/0.40 tff(156,plain,
% 0.18/0.40 (![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.18/0.41 tff(157,plain,
% 0.18/0.41 (p7(c9, c10) <=> p7(c9, c10)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(158,axiom,(p7(c9, c10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_5')).
% 0.18/0.41 tff(159,plain,
% 0.18/0.41 (p7(c9, c10)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.18/0.41 tff(160,plain,
% 0.18/0.41 (((~![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))) | ((~p2(c16, c16)) | (~p2(c15, c15)) | (~p2(f4(c16, c14), f5(f6(c9), c20))) | (~p7(c9, c10)) | (~p2(f4(c15, c14), f5(f6(c9), c19))))) <=> ((~![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))) | (~p2(c16, c16)) | (~p2(c15, c15)) | (~p2(f4(c16, c14), f5(f6(c9), c20))) | (~p7(c9, c10)) | (~p2(f4(c15, c14), f5(f6(c9), c19))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(161,plain,
% 0.18/0.41 (((~p2(f4(c16, c14), f5(f6(c9), c20))) | (~p2(f4(c15, c14), f5(f6(c9), c19))) | (~p2(c16, c16)) | (~p2(c15, c15)) | (~p7(c9, c10))) <=> ((~p2(c16, c16)) | (~p2(c15, c15)) | (~p2(f4(c16, c14), f5(f6(c9), c20))) | (~p7(c9, c10)) | (~p2(f4(c15, c14), f5(f6(c9), c19))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(162,plain,
% 0.18/0.41 (((~![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))) | ((~p2(f4(c16, c14), f5(f6(c9), c20))) | (~p2(f4(c15, c14), f5(f6(c9), c19))) | (~p2(c16, c16)) | (~p2(c15, c15)) | (~p7(c9, c10)))) <=> ((~![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))) | ((~p2(c16, c16)) | (~p2(c15, c15)) | (~p2(f4(c16, c14), f5(f6(c9), c20))) | (~p7(c9, c10)) | (~p2(f4(c15, c14), f5(f6(c9), c19)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[161])).
% 0.18/0.41 tff(163,plain,
% 0.18/0.41 (((~![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))) | ((~p2(f4(c16, c14), f5(f6(c9), c20))) | (~p2(f4(c15, c14), f5(f6(c9), c19))) | (~p2(c16, c16)) | (~p2(c15, c15)) | (~p7(c9, c10)))) <=> ((~![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))) | (~p2(c16, c16)) | (~p2(c15, c15)) | (~p2(f4(c16, c14), f5(f6(c9), c20))) | (~p7(c9, c10)) | (~p2(f4(c15, c14), f5(f6(c9), c19))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[162, 160])).
% 0.18/0.41 tff(164,plain,
% 0.18/0.41 ((~![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))) | ((~p2(f4(c16, c14), f5(f6(c9), c20))) | (~p2(f4(c15, c14), f5(f6(c9), c19))) | (~p2(c16, c16)) | (~p2(c15, c15)) | (~p7(c9, c10)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(165,plain,
% 0.18/0.41 ((~![X32: $i, X34: $i, X33: $i] : ((~p2(f4(X33, c14), f5(f6(X34), c20))) | (~p2(f4(X32, c14), f5(f6(X34), c19))) | (~p2(c16, X33)) | (~p2(c15, X32)) | (~p7(X34, c10)))) | (~p2(c16, c16)) | (~p2(c15, c15)) | (~p2(f4(c16, c14), f5(f6(c9), c20))) | (~p7(c9, c10)) | (~p2(f4(c15, c14), f5(f6(c9), c19)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.18/0.41 tff(166,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[165, 159, 156, 62, 124, 146, 97])).
% 0.18/0.41 % SZS output end Proof
% 0.18/0.41 % E exiting
%------------------------------------------------------------------------------