%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN631-1 : 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 05:39:43 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
% 0.03/0.12 % Problem : SYN631-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % 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 12:41:12 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(p5_type, type, (
% 0.18/0.37 p5: ( $i * $i ) > $o)).
% 0.18/0.37 tff(f18_type, type, (
% 0.18/0.37 f18: ( $i * $i ) > $i)).
% 0.18/0.37 tff(f19_type, type, (
% 0.18/0.37 f19: ( $i * $i * $i ) > $i)).
% 0.18/0.37 tff(f14_type, type, (
% 0.18/0.37 f14: $i > $i)).
% 0.18/0.37 tff(c28_type, type, (
% 0.18/0.37 c28: $i)).
% 0.18/0.37 tff(c27_type, type, (
% 0.18/0.37 c27: $i)).
% 0.18/0.37 tff(c24_type, type, (
% 0.18/0.37 c24: $i)).
% 0.18/0.37 tff(f20_type, type, (
% 0.18/0.37 f20: $i > $i)).
% 0.18/0.37 tff(c29_type, type, (
% 0.18/0.37 c29: $i)).
% 0.18/0.37 tff(p12_type, type, (
% 0.18/0.37 p12: ( $i * $i ) > $o)).
% 0.18/0.37 tff(f13_type, type, (
% 0.18/0.37 f13: ( $i * $i ) > $i)).
% 0.18/0.37 tff(f16_type, type, (
% 0.18/0.37 f16: $i > $i)).
% 0.18/0.37 tff(p23_type, type, (
% 0.18/0.37 p23: ( $i * $i ) > $o)).
% 0.18/0.37 tff(f11_type, type, (
% 0.18/0.37 f11: $i > $i)).
% 0.18/0.37 tff(f15_type, type, (
% 0.18/0.37 f15: $i > $i)).
% 0.18/0.37 tff(p10_type, type, (
% 0.18/0.37 p10: ( $i * $i ) > $o)).
% 0.18/0.37 tff(p9_type, type, (
% 0.18/0.37 p9: ( $i * $i ) > $o)).
% 0.18/0.37 tff(1,assumption,(p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))), introduced(assumption)).
% 0.18/0.37 tff(2,assumption,(~p5(c27, c27)), introduced(assumption)).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (^[X37: $i] : refl(p5(X37, X37) <=> p5(X37, X37))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![X37: $i] : p5(X37, X37) <=> ![X37: $i] : p5(X37, X37)),
% 0.18/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![X37: $i] : p5(X37, X37) <=> ![X37: $i] : p5(X37, X37)),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(6,axiom,(![X37: $i] : p5(X37, X37)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_5')).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![X37: $i] : p5(X37, X37)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.37 tff(8,plain,(
% 0.18/0.37 ![X37: $i] : p5(X37, X37)),
% 0.18/0.37 inference(skolemize,[status(sab)],[7])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (![X37: $i] : p5(X37, X37)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 ((~![X37: $i] : p5(X37, X37)) | p5(c27, c27)),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.18/0.37 tff(12,plain,(p5(c27, c27)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (^[X39: $i, X38: $i, X37: $i] : refl(((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39)) <=> ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39)))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39)) <=> ![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39)) <=> ![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (^[X39: $i, X38: $i, X37: $i] : trans(monotonicity(rewrite((p5(X38, X39) | (~p5(X37, X38))) <=> ((~p5(X37, X38)) | p5(X38, X39))), (((p5(X38, X39) | (~p5(X37, X38))) | (~p5(X37, X39))) <=> (((~p5(X37, X38)) | p5(X38, X39)) | (~p5(X37, X39))))), rewrite((((~p5(X37, X38)) | p5(X38, X39)) | (~p5(X37, X39))) <=> ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))), (((p5(X38, X39) | (~p5(X37, X38))) | (~p5(X37, X39))) <=> ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (![X39: $i, X38: $i, X37: $i] : ((p5(X38, X39) | (~p5(X37, X38))) | (~p5(X37, X39))) <=> ![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.37 tff(18,axiom,(![X39: $i, X38: $i, X37: $i] : ((p5(X38, X39) | (~p5(X37, X38))) | (~p5(X37, X39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_25')).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.37 tff(21,plain,(
% 0.18/0.37 ![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))),
% 0.18/0.37 inference(skolemize,[status(sab)],[20])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | ((~p5(c27, c27)) | (~p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))) | p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27))) <=> ((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | (~p5(c27, c27)) | (~p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))) | p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 (((~p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))) | (~p5(c27, c27)) | p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27)) <=> ((~p5(c27, c27)) | (~p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))) | p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | ((~p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))) | (~p5(c27, c27)) | p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27))) <=> ((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | ((~p5(c27, c27)) | (~p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))) | p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27)))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 (((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | ((~p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))) | (~p5(c27, c27)) | p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27))) <=> ((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | (~p5(c27, c27)) | (~p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))) | p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27))),
% 0.18/0.37 inference(transitivity,[status(thm)],[25, 23])).
% 0.18/0.37 tff(27,plain,
% 0.18/0.37 ((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | ((~p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))) | (~p5(c27, c27)) | p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 ((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | (~p5(c27, c27)) | (~p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))) | p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[28, 22, 12, 1])).
% 0.18/0.37 tff(30,plain,
% 0.18/0.37 (^[X43: $i, X42: $i] : refl(((~p5(X42, X43)) | p5(f16(X42), f16(X43))) <=> ((~p5(X42, X43)) | p5(f16(X42), f16(X43))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43))) <=> ![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[30])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43))) <=> ![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (^[X43: $i, X42: $i] : rewrite((p5(f16(X42), f16(X43)) | (~p5(X42, X43))) <=> ((~p5(X42, X43)) | p5(f16(X42), f16(X43))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 (![X43: $i, X42: $i] : (p5(f16(X42), f16(X43)) | (~p5(X42, X43))) <=> ![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.18/0.37 tff(35,axiom,(![X43: $i, X42: $i] : (p5(f16(X42), f16(X43)) | (~p5(X42, X43)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_18')).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.18/0.37 tff(38,plain,(
% 0.18/0.37 ![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[37])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 (![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.18/0.38 tff(40,plain,
% 0.18/0.38 (((~![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43)))) | ((~p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27)) | p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27)))) <=> ((~![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43)))) | (~p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27)) | p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 ((~![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43)))) | ((~p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27)) | p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 ((~![X43: $i, X42: $i] : ((~p5(X42, X43)) | p5(f16(X42), f16(X43)))) | (~p5(f18(f20(c29), f19(c24, c27, f14(c28))), c27)) | p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 (p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[42, 39, 29])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 (^[X45: $i, X44: $i] : refl(p5(f16(f18(X44, X45)), X45) <=> p5(f16(f18(X44, X45)), X45))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 (![X45: $i, X44: $i] : p5(f16(f18(X44, X45)), X45) <=> ![X45: $i, X44: $i] : p5(f16(f18(X44, X45)), X45)),
% 0.18/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (![X45: $i, X44: $i] : p5(f16(f18(X44, X45)), X45) <=> ![X45: $i, X44: $i] : p5(f16(f18(X44, X45)), X45)),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(47,axiom,(![X45: $i, X44: $i] : p5(f16(f18(X44, X45)), X45)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_11')).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (![X45: $i, X44: $i] : p5(f16(f18(X44, X45)), X45)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.18/0.38 tff(49,plain,(
% 0.18/0.38 ![X45: $i, X44: $i] : p5(f16(f18(X44, X45)), X45)),
% 0.18/0.38 inference(skolemize,[status(sab)],[48])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 (![X45: $i, X44: $i] : p5(f16(f18(X44, X45)), X45)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 ((~![X45: $i, X44: $i] : p5(f16(f18(X44, X45)), X45)) | p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(52,plain,
% 0.18/0.38 (p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 (((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | (p5(f19(c24, c27, f14(c28)), f16(c27)) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28)))) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27))))) <=> ((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | p5(f19(c24, c27, f14(c28)), f16(c27)) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28)))) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(54,plain,
% 0.18/0.38 (((~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28)))) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27))) | p5(f19(c24, c27, f14(c28)), f16(c27))) <=> (p5(f19(c24, c27, f14(c28)), f16(c27)) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28)))) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(55,plain,
% 0.18/0.38 (((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | ((~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28)))) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27))) | p5(f19(c24, c27, f14(c28)), f16(c27)))) <=> ((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | (p5(f19(c24, c27, f14(c28)), f16(c27)) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28)))) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27)))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[54])).
% 0.18/0.38 tff(56,plain,
% 0.18/0.38 (((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | ((~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28)))) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27))) | p5(f19(c24, c27, f14(c28)), f16(c27)))) <=> ((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | p5(f19(c24, c27, f14(c28)), f16(c27)) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28)))) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[55, 53])).
% 0.18/0.38 tff(57,plain,
% 0.18/0.38 ((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | ((~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28)))) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27))) | p5(f19(c24, c27, f14(c28)), f16(c27)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(58,plain,
% 0.18/0.38 ((~![X39: $i, X38: $i, X37: $i] : ((~p5(X37, X38)) | (~p5(X37, X39)) | p5(X38, X39))) | p5(f19(c24, c27, f14(c28)), f16(c27)) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f19(c24, c27, f14(c28)))) | (~p5(f16(f18(f20(c29), f19(c24, c27, f14(c28)))), f16(c27)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.18/0.38 tff(59,plain,
% 0.18/0.38 (p5(f19(c24, c27, f14(c28)), f16(c27))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[58, 22, 52, 43])).
% 0.18/0.38 tff(60,assumption,(~p5(f14(c28), f14(c28))), introduced(assumption)).
% 0.18/0.38 tff(61,plain,
% 0.18/0.38 ((~![X37: $i] : p5(X37, X37)) | p5(f14(c28), f14(c28))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(62,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[61, 9, 60])).
% 0.18/0.38 tff(63,plain,(p5(f14(c28), f14(c28))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(64,plain,
% 0.18/0.38 (^[X9: $i, X11: $i, X10: $i, X8: $i] : refl(((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11))) <=> ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(65,plain,
% 0.18/0.38 (![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11))) <=> ![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[64])).
% 0.18/0.38 tff(66,plain,
% 0.18/0.38 (![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11))) <=> ![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(67,plain,
% 0.18/0.38 (^[X9: $i, X11: $i, X10: $i, X8: $i] : trans(monotonicity(rewrite((p12(f13(X8, X9), f13(X10, X11)) | (~p5(X8, X10))) <=> ((~p5(X8, X10)) | p12(f13(X8, X9), f13(X10, X11)))), (((p12(f13(X8, X9), f13(X10, X11)) | (~p5(X8, X10))) | (~p5(X9, X11))) <=> (((~p5(X8, X10)) | p12(f13(X8, X9), f13(X10, X11))) | (~p5(X9, X11))))), rewrite((((~p5(X8, X10)) | p12(f13(X8, X9), f13(X10, X11))) | (~p5(X9, X11))) <=> ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))), (((p12(f13(X8, X9), f13(X10, X11)) | (~p5(X8, X10))) | (~p5(X9, X11))) <=> ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(68,plain,
% 0.18/0.38 (![X9: $i, X11: $i, X10: $i, X8: $i] : ((p12(f13(X8, X9), f13(X10, X11)) | (~p5(X8, X10))) | (~p5(X9, X11))) <=> ![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[67])).
% 0.18/0.38 tff(69,axiom,(![X9: $i, X11: $i, X10: $i, X8: $i] : ((p12(f13(X8, X9), f13(X10, X11)) | (~p5(X8, X10))) | (~p5(X9, X11)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_32')).
% 0.18/0.38 tff(70,plain,
% 0.18/0.38 (![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.18/0.38 tff(71,plain,
% 0.18/0.38 (![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.18/0.38 tff(72,plain,(
% 0.18/0.38 ![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[71])).
% 0.18/0.38 tff(73,plain,
% 0.18/0.38 (![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.18/0.38 tff(74,plain,
% 0.18/0.38 (((~![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))) | ((~p5(f14(c28), f14(c28))) | (~p5(f19(c24, c27, f14(c28)), f16(c27))) | p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28))))) <=> ((~![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))) | (~p5(f14(c28), f14(c28))) | (~p5(f19(c24, c27, f14(c28)), f16(c27))) | p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(75,plain,
% 0.18/0.38 (((~p5(f19(c24, c27, f14(c28)), f16(c27))) | (~p5(f14(c28), f14(c28))) | p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))) <=> ((~p5(f14(c28), f14(c28))) | (~p5(f19(c24, c27, f14(c28)), f16(c27))) | p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(76,plain,
% 0.18/0.38 (((~![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))) | ((~p5(f19(c24, c27, f14(c28)), f16(c27))) | (~p5(f14(c28), f14(c28))) | p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28))))) <=> ((~![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))) | ((~p5(f14(c28), f14(c28))) | (~p5(f19(c24, c27, f14(c28)), f16(c27))) | p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[75])).
% 0.18/0.38 tff(77,plain,
% 0.18/0.38 (((~![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))) | ((~p5(f19(c24, c27, f14(c28)), f16(c27))) | (~p5(f14(c28), f14(c28))) | p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28))))) <=> ((~![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))) | (~p5(f14(c28), f14(c28))) | (~p5(f19(c24, c27, f14(c28)), f16(c27))) | p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[76, 74])).
% 0.18/0.38 tff(78,plain,
% 0.18/0.38 ((~![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))) | ((~p5(f19(c24, c27, f14(c28)), f16(c27))) | (~p5(f14(c28), f14(c28))) | p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(79,plain,
% 0.18/0.38 ((~![X9: $i, X11: $i, X10: $i, X8: $i] : ((~p5(X8, X10)) | (~p5(X9, X11)) | p12(f13(X8, X9), f13(X10, X11)))) | (~p5(f14(c28), f14(c28))) | (~p5(f19(c24, c27, f14(c28)), f16(c27))) | p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.18/0.38 tff(80,plain,
% 0.18/0.38 ((~p5(f19(c24, c27, f14(c28)), f16(c27))) | p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[79, 73, 63])).
% 0.18/0.38 tff(81,plain,
% 0.18/0.38 (p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[80, 59])).
% 0.18/0.38 tff(82,plain,
% 0.18/0.38 (^[X31: $i, X30: $i, X29: $i] : refl(((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29))) <=> ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(83,plain,
% 0.18/0.38 (![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29))) <=> ![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[82])).
% 0.18/0.38 tff(84,plain,
% 0.18/0.39 (![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29))) <=> ![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(85,plain,
% 0.18/0.39 (^[X31: $i, X30: $i, X29: $i] : rewrite((p23(f13(f19(X29, X30, X31), X31), f11(X29)) | (~p23(f13(X30, X31), f11(f15(X29))))) <=> ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 (![X31: $i, X30: $i, X29: $i] : (p23(f13(f19(X29, X30, X31), X31), f11(X29)) | (~p23(f13(X30, X31), f11(f15(X29))))) <=> ![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[85])).
% 0.18/0.39 tff(87,axiom,(![X31: $i, X30: $i, X29: $i] : (p23(f13(f19(X29, X30, X31), X31), f11(X29)) | (~p23(f13(X30, X31), f11(f15(X29)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p23_35')).
% 0.18/0.39 tff(88,plain,
% 0.18/0.39 (![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 (![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.18/0.39 tff(90,plain,(
% 0.18/0.39 ![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[89])).
% 0.18/0.39 tff(91,plain,
% 0.18/0.39 (![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 (p23(f13(c27, f14(c28)), f11(f15(c24))) <=> p23(f13(c27, f14(c28)), f11(f15(c24)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(93,axiom,(p23(f13(c27, f14(c28)), f11(f15(c24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p23_12')).
% 0.18/0.39 tff(94,plain,
% 0.18/0.39 (p23(f13(c27, f14(c28)), f11(f15(c24)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.18/0.39 tff(95,plain,
% 0.18/0.39 (((~![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29)))) | ((~p23(f13(c27, f14(c28)), f11(f15(c24)))) | p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24)))) <=> ((~![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29)))) | (~p23(f13(c27, f14(c28)), f11(f15(c24)))) | p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(96,plain,
% 0.18/0.39 ((~![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29)))) | ((~p23(f13(c27, f14(c28)), f11(f15(c24)))) | p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(97,plain,
% 0.18/0.39 ((~![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p23(f13(f19(X29, X30, X31), X31), f11(X29)))) | (~p23(f13(c27, f14(c28)), f11(f15(c24)))) | p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.18/0.39 tff(98,plain,
% 0.18/0.39 (p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[97, 94, 91])).
% 0.18/0.39 tff(99,assumption,(~p9(c24, c24)), introduced(assumption)).
% 0.18/0.39 tff(100,plain,
% 0.18/0.39 (^[X74: $i] : refl(p9(X74, X74) <=> p9(X74, X74))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(101,plain,
% 0.18/0.39 (![X74: $i] : p9(X74, X74) <=> ![X74: $i] : p9(X74, X74)),
% 0.18/0.39 inference(quant_intro,[status(thm)],[100])).
% 0.18/0.39 tff(102,plain,
% 0.18/0.39 (![X74: $i] : p9(X74, X74) <=> ![X74: $i] : p9(X74, X74)),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(103,axiom,(![X74: $i] : p9(X74, X74)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_2')).
% 0.18/0.39 tff(104,plain,
% 0.18/0.39 (![X74: $i] : p9(X74, X74)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.18/0.39 tff(105,plain,(
% 0.18/0.39 ![X74: $i] : p9(X74, X74)),
% 0.18/0.39 inference(skolemize,[status(sab)],[104])).
% 0.18/0.39 tff(106,plain,
% 0.18/0.39 (![X74: $i] : p9(X74, X74)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.18/0.39 tff(107,plain,
% 0.18/0.39 ((~![X74: $i] : p9(X74, X74)) | p9(c24, c24)),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(108,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[107, 106, 99])).
% 0.18/0.39 tff(109,plain,(p9(c24, c24)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(110,plain,
% 0.18/0.39 (^[X4: $i, X3: $i] : refl(((~p9(X3, X4)) | p10(f11(X3), f11(X4))) <=> ((~p9(X3, X4)) | p10(f11(X3), f11(X4))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(111,plain,
% 0.18/0.39 (![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4))) <=> ![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[110])).
% 0.18/0.39 tff(112,plain,
% 0.18/0.39 (![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4))) <=> ![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(113,plain,
% 0.18/0.39 (^[X4: $i, X3: $i] : rewrite((p10(f11(X3), f11(X4)) | (~p9(X3, X4))) <=> ((~p9(X3, X4)) | p10(f11(X3), f11(X4))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(114,plain,
% 0.18/0.39 (![X4: $i, X3: $i] : (p10(f11(X3), f11(X4)) | (~p9(X3, X4))) <=> ![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[113])).
% 0.18/0.39 tff(115,axiom,(![X4: $i, X3: $i] : (p10(f11(X3), f11(X4)) | (~p9(X3, X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_15')).
% 0.18/0.39 tff(116,plain,
% 0.18/0.39 (![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.18/0.39 tff(117,plain,
% 0.18/0.39 (![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.18/0.39 tff(118,plain,(
% 0.18/0.39 ![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[117])).
% 0.18/0.39 tff(119,plain,
% 0.18/0.39 (![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.18/0.39 tff(120,plain,
% 0.18/0.39 (((~![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))) | ((~p9(c24, c24)) | p10(f11(c24), f11(c24)))) <=> ((~![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))) | (~p9(c24, c24)) | p10(f11(c24), f11(c24)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(121,plain,
% 0.18/0.39 ((~![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))) | ((~p9(c24, c24)) | p10(f11(c24), f11(c24)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(122,plain,
% 0.18/0.39 ((~![X4: $i, X3: $i] : ((~p9(X3, X4)) | p10(f11(X3), f11(X4)))) | (~p9(c24, c24)) | p10(f11(c24), f11(c24))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.18/0.39 tff(123,plain,
% 0.18/0.39 (p10(f11(c24), f11(c24))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[122, 119, 109])).
% 0.18/0.39 tff(124,plain,
% 0.18/0.39 (^[X25: $i, X27: $i, X28: $i, X26: $i] : refl(((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26)) <=> ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(125,plain,
% 0.18/0.39 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26)) <=> ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[124])).
% 0.18/0.39 tff(126,plain,
% 0.18/0.39 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26)) <=> ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(127,plain,
% 0.18/0.39 (^[X25: $i, X27: $i, X28: $i, X26: $i] : trans(monotonicity(trans(monotonicity(rewrite((p23(X25, X26) | (~p12(X28, X25))) <=> ((~p12(X28, X25)) | p23(X25, X26))), (((p23(X25, X26) | (~p12(X28, X25))) | (~p23(X28, X27))) <=> (((~p12(X28, X25)) | p23(X25, X26)) | (~p23(X28, X27))))), rewrite((((~p12(X28, X25)) | p23(X25, X26)) | (~p23(X28, X27))) <=> ((~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))), (((p23(X25, X26) | (~p12(X28, X25))) | (~p23(X28, X27))) <=> ((~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26)))), ((((p23(X25, X26) | (~p12(X28, X25))) | (~p23(X28, X27))) | (~p10(X27, X26))) <=> (((~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26)) | (~p10(X27, X26))))), rewrite((((~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26)) | (~p10(X27, X26))) <=> ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))), ((((p23(X25, X26) | (~p12(X28, X25))) | (~p23(X28, X27))) | (~p10(X27, X26))) <=> ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(128,plain,
% 0.18/0.39 (![X25: $i, X27: $i, X28: $i, X26: $i] : (((p23(X25, X26) | (~p12(X28, X25))) | (~p23(X28, X27))) | (~p10(X27, X26))) <=> ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[127])).
% 0.18/0.39 tff(129,axiom,(![X25: $i, X27: $i, X28: $i, X26: $i] : (((p23(X25, X26) | (~p12(X28, X25))) | (~p23(X28, X27))) | (~p10(X27, X26)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p23_29')).
% 0.18/0.39 tff(130,plain,
% 0.18/0.39 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.18/0.39 tff(131,plain,
% 0.18/0.39 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.18/0.39 tff(132,plain,(
% 0.18/0.39 ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))),
% 0.18/0.39 inference(skolemize,[status(sab)],[131])).
% 0.18/0.39 tff(133,plain,
% 0.18/0.39 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.18/0.39 tff(134,plain,
% 0.18/0.39 ((~p23(f13(f16(c27), f14(c28)), f11(c24))) <=> (~p23(f13(f16(c27), f14(c28)), f11(c24)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(135,axiom,(~p23(f13(f16(c27), f14(c28)), f11(c24))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p23_13')).
% 0.18/0.39 tff(136,plain,
% 0.18/0.39 (~p23(f13(f16(c27), f14(c28)), f11(c24))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.18/0.39 tff(137,plain,
% 0.18/0.39 (((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))) | (p23(f13(f16(c27), f14(c28)), f11(c24)) | (~p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))) | (~p10(f11(c24), f11(c24))) | (~p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))))) <=> ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))) | p23(f13(f16(c27), f14(c28)), f11(c24)) | (~p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))) | (~p10(f11(c24), f11(c24))) | (~p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(138,plain,
% 0.18/0.39 (((~p10(f11(c24), f11(c24))) | (~p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))) | (~p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))) | p23(f13(f16(c27), f14(c28)), f11(c24))) <=> (p23(f13(f16(c27), f14(c28)), f11(c24)) | (~p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))) | (~p10(f11(c24), f11(c24))) | (~p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(139,plain,
% 0.18/0.39 (((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))) | ((~p10(f11(c24), f11(c24))) | (~p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))) | (~p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))) | p23(f13(f16(c27), f14(c28)), f11(c24)))) <=> ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))) | (p23(f13(f16(c27), f14(c28)), f11(c24)) | (~p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))) | (~p10(f11(c24), f11(c24))) | (~p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28))))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[138])).
% 0.18/0.40 tff(140,plain,
% 0.18/0.40 (((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))) | ((~p10(f11(c24), f11(c24))) | (~p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))) | (~p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))) | p23(f13(f16(c27), f14(c28)), f11(c24)))) <=> ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))) | p23(f13(f16(c27), f14(c28)), f11(c24)) | (~p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))) | (~p10(f11(c24), f11(c24))) | (~p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[139, 137])).
% 0.18/0.40 tff(141,plain,
% 0.18/0.40 ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))) | ((~p10(f11(c24), f11(c24))) | (~p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))) | (~p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28)))) | p23(f13(f16(c27), f14(c28)), f11(c24)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(142,plain,
% 0.18/0.40 ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p10(X27, X26)) | (~p23(X28, X27)) | (~p12(X28, X25)) | p23(X25, X26))) | p23(f13(f16(c27), f14(c28)), f11(c24)) | (~p23(f13(f19(c24, c27, f14(c28)), f14(c28)), f11(c24))) | (~p10(f11(c24), f11(c24))) | (~p12(f13(f19(c24, c27, f14(c28)), f14(c28)), f13(f16(c27), f14(c28))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.18/0.40 tff(143,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[142, 136, 133, 123, 98, 81])).
% 0.18/0.40 tff(144,plain,(~p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(145,plain,
% 0.18/0.40 (^[X31: $i, X30: $i, X29: $i] : refl(((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31)))) <=> ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(146,plain,
% 0.18/0.40 (![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31)))) <=> ![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[145])).
% 0.18/0.40 tff(147,plain,
% 0.18/0.40 (![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31)))) <=> ![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(148,plain,
% 0.18/0.40 (^[X31: $i, X30: $i, X29: $i] : rewrite((p5(X30, f18(f20(c29), f19(X29, X30, X31))) | (~p23(f13(X30, X31), f11(f15(X29))))) <=> ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(149,plain,
% 0.18/0.40 (![X31: $i, X30: $i, X29: $i] : (p5(X30, f18(f20(c29), f19(X29, X30, X31))) | (~p23(f13(X30, X31), f11(f15(X29))))) <=> ![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[148])).
% 0.18/0.40 tff(150,axiom,(![X31: $i, X30: $i, X29: $i] : (p5(X30, f18(f20(c29), f19(X29, X30, X31))) | (~p23(f13(X30, X31), f11(f15(X29)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_34')).
% 0.18/0.40 tff(151,plain,
% 0.18/0.40 (![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.18/0.40 tff(152,plain,
% 0.18/0.40 (![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.18/0.40 tff(153,plain,(
% 0.18/0.40 ![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[152])).
% 0.18/0.40 tff(154,plain,
% 0.18/0.40 (![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[153, 146])).
% 0.18/0.40 tff(155,plain,
% 0.18/0.40 (((~![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31))))) | ((~p23(f13(c27, f14(c28)), f11(f15(c24)))) | p5(c27, f18(f20(c29), f19(c24, c27, f14(c28)))))) <=> ((~![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31))))) | (~p23(f13(c27, f14(c28)), f11(f15(c24)))) | p5(c27, f18(f20(c29), f19(c24, c27, f14(c28)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(156,plain,
% 0.18/0.40 ((~![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31))))) | ((~p23(f13(c27, f14(c28)), f11(f15(c24)))) | p5(c27, f18(f20(c29), f19(c24, c27, f14(c28)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(157,plain,
% 0.18/0.40 ((~![X31: $i, X30: $i, X29: $i] : ((~p23(f13(X30, X31), f11(f15(X29)))) | p5(X30, f18(f20(c29), f19(X29, X30, X31))))) | (~p23(f13(c27, f14(c28)), f11(f15(c24)))) | p5(c27, f18(f20(c29), f19(c24, c27, f14(c28))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.18/0.40 tff(158,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[157, 94, 154, 144])).
% 0.18/0.40 % SZS output end Proof
% 0.18/0.40 % E exiting
%------------------------------------------------------------------------------