%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN678-1 : TPTP v9.0.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:39:49 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN678-1 : TPTP v9.0.0. Released v2.5.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n013.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 12:40:38 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(p2_type, type, (
% 0.11/0.38 p2: ( $i * $i ) > $o)).
% 0.11/0.38 tff(f11_type, type, (
% 0.11/0.38 f11: ( $i * $i ) > $i)).
% 0.11/0.38 tff(c34_type, type, (
% 0.11/0.38 c34: $i)).
% 0.11/0.38 tff(f4_type, type, (
% 0.11/0.38 f4: $i > $i)).
% 0.11/0.38 tff(c33_type, type, (
% 0.11/0.38 c33: $i)).
% 0.11/0.38 tff(c32_type, type, (
% 0.11/0.38 c32: $i)).
% 0.11/0.38 tff(p3_type, type, (
% 0.11/0.38 p3: ( $i * $i ) > $o)).
% 0.11/0.38 tff(p10_type, type, (
% 0.11/0.38 p10: ( $i * $i ) > $o)).
% 0.11/0.38 tff(c35_type, type, (
% 0.11/0.38 c35: $i)).
% 0.11/0.38 tff(p25_type, type, (
% 0.11/0.38 p25: ( $i * $i ) > $o)).
% 0.11/0.38 tff(c36_type, type, (
% 0.11/0.38 c36: $i)).
% 0.11/0.38 tff(f16_type, type, (
% 0.11/0.38 f16: ( $i * $i ) > $i)).
% 0.11/0.38 tff(f9_type, type, (
% 0.11/0.38 f9: $i > $i)).
% 0.11/0.38 tff(f17_type, type, (
% 0.11/0.38 f17: $i > $i)).
% 0.11/0.38 tff(c31_type, type, (
% 0.11/0.38 c31: $i)).
% 0.11/0.38 tff(1,assumption,(~p3(f4(c33), f4(c33))), introduced(assumption)).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (^[X83: $i] : refl(p3(X83, X83) <=> p3(X83, X83))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![X83: $i] : p3(X83, X83) <=> ![X83: $i] : p3(X83, X83)),
% 0.11/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (![X83: $i] : p3(X83, X83) <=> ![X83: $i] : p3(X83, X83)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(5,axiom,(![X83: $i] : p3(X83, X83)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_5')).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 (![X83: $i] : p3(X83, X83)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.38 tff(7,plain,(
% 0.11/0.38 ![X83: $i] : p3(X83, X83)),
% 0.11/0.38 inference(skolemize,[status(sab)],[6])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 (![X83: $i] : p3(X83, X83)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 ((~![X83: $i] : p3(X83, X83)) | p3(f4(c33), f4(c33))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.11/0.38 tff(11,plain,(p3(f4(c33), f4(c33))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (^[X0: $i, X2: $i, X1: $i] : refl(((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2)) <=> ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2)) <=> ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 (^[X0: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((p10(X1, X2) | (~p10(X0, X1))) <=> ((~p10(X0, X1)) | p10(X1, X2))), (((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))) <=> (((~p10(X0, X1)) | p10(X1, X2)) | (~p10(X0, X2))))), rewrite((((~p10(X0, X1)) | p10(X1, X2)) | (~p10(X0, X2))) <=> ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))), (((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))) <=> ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (![X0: $i, X2: $i, X1: $i] : ((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.11/0.38 tff(17,axiom,(![X0: $i, X2: $i, X1: $i] : ((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_26')).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.11/0.38 tff(19,plain,
% 0.11/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.11/0.38 tff(20,plain,(
% 0.11/0.38 ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.11/0.38 inference(skolemize,[status(sab)],[19])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (p10(c35, c34) <=> p10(c35, c34)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(23,axiom,(p10(c35, c34)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p10_11')).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (p10(c35, c34)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(c35, c34)) | p10(c34, c34))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(c35, c34)) | p10(c34, c34))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (((~p10(c35, c34)) | (~p10(c35, c34)) | p10(c34, c34)) <=> ((~p10(c35, c34)) | p10(c34, c34))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(c35, c34)) | (~p10(c35, c34)) | p10(c34, c34))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(c35, c34)) | p10(c34, c34)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[26])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(c35, c34)) | (~p10(c35, c34)) | p10(c34, c34))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(c35, c34)) | p10(c34, c34))),
% 0.11/0.38 inference(transitivity,[status(thm)],[27, 25])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(c35, c34)) | (~p10(c35, c34)) | p10(c34, c34))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(c35, c34)) | p10(c34, c34)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (p10(c34, c34)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[30, 24, 21])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (^[X31: $i, X32: $i, X34: $i, X33: $i] : refl(((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34))) <=> ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(35,plain,
% 0.11/0.38 (^[X31: $i, X32: $i, X34: $i, X33: $i] : trans(monotonicity(rewrite((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) <=> ((~p10(X32, X34)) | p2(f11(X31, X32), f11(X33, X34)))), (((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) | (~p3(X31, X33))) <=> (((~p10(X32, X34)) | p2(f11(X31, X32), f11(X33, X34))) | (~p3(X31, X33))))), rewrite((((~p10(X32, X34)) | p2(f11(X31, X32), f11(X33, X34))) | (~p3(X31, X33))) <=> ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))), (((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) | (~p3(X31, X33))) <=> ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) | (~p3(X31, X33))) <=> ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.11/0.38 tff(37,axiom,(![X31: $i, X32: $i, X34: $i, X33: $i] : ((p2(f11(X31, X32), f11(X33, X34)) | (~p10(X32, X34))) | (~p3(X31, X33)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_47')).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.11/0.39 tff(40,plain,(
% 0.11/0.39 ![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[39])).
% 0.11/0.39 tff(41,plain,
% 0.11/0.39 (![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.11/0.39 tff(42,plain,
% 0.11/0.39 (((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))) | ((~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))) <=> ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))) | (~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(43,plain,
% 0.11/0.39 ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))) | ((~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(44,plain,
% 0.11/0.39 ((~![X31: $i, X32: $i, X34: $i, X33: $i] : ((~p10(X32, X34)) | (~p3(X31, X33)) | p2(f11(X31, X32), f11(X33, X34)))) | (~p10(c34, c34)) | (~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.11/0.39 tff(45,plain,
% 0.11/0.39 ((~p3(f4(c33), f4(c33))) | p2(f11(f4(c33), c34), f11(f4(c33), c34))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[44, 41, 31])).
% 0.11/0.39 tff(46,plain,
% 0.11/0.39 (p2(f11(f4(c33), c34), f11(f4(c33), c34))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[45, 11])).
% 0.11/0.39 tff(47,plain,
% 0.11/0.39 (^[X36: $i] : refl(((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) <=> ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(48,plain,
% 0.11/0.39 (![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) <=> ![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.11/0.39 tff(49,plain,
% 0.11/0.39 (![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) <=> ![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(50,plain,
% 0.11/0.39 (^[X36: $i] : trans(monotonicity(rewrite((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) <=> (p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))), (((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) | (~p25(c32, X36))) <=> ((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) | (~p25(c32, X36))))), rewrite(((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) | (~p25(c32, X36))) <=> ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))), (((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) | (~p25(c32, X36))) <=> ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(51,plain,
% 0.11/0.39 (![X36: $i] : ((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) | (~p25(c32, X36))) <=> ![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.11/0.39 tff(52,axiom,(![X36: $i] : ((p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36))) | (~p25(c32, X36)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_51')).
% 0.11/0.39 tff(53,plain,
% 0.11/0.39 (![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.11/0.39 tff(54,plain,
% 0.11/0.39 (![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.11/0.39 tff(55,plain,(
% 0.11/0.39 ![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[54])).
% 0.11/0.39 tff(56,plain,
% 0.11/0.39 (![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.11/0.39 tff(57,plain,
% 0.11/0.39 (p25(c32, c33) <=> p25(c32, c33)),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(58,axiom,(p25(c32, c33)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p25_14')).
% 0.11/0.39 tff(59,plain,
% 0.11/0.39 (p25(c32, c33)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.11/0.39 tff(60,plain,
% 0.11/0.39 (p25(c33, c36) <=> p25(c33, c36)),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(61,axiom,(p25(c33, c36)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p25_12')).
% 0.11/0.39 tff(62,plain,
% 0.11/0.39 (p25(c33, c36)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.11/0.39 tff(63,plain,
% 0.11/0.39 (((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | (p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36)))) <=> ((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(64,plain,
% 0.11/0.39 (((~p25(c32, c33)) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c33, c36))) <=> (p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(65,plain,
% 0.11/0.39 (((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | ((~p25(c32, c33)) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c33, c36)))) <=> ((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | (p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36))))),
% 0.11/0.39 inference(monotonicity,[status(thm)],[64])).
% 0.11/0.39 tff(66,plain,
% 0.11/0.39 (((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | ((~p25(c32, c33)) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c33, c36)))) <=> ((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36)))),
% 0.11/0.39 inference(transitivity,[status(thm)],[65, 63])).
% 0.11/0.39 tff(67,plain,
% 0.11/0.39 ((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | ((~p25(c32, c33)) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c33, c36)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(68,plain,
% 0.11/0.39 ((~![X36: $i] : ((~p25(c32, X36)) | p2(f11(f4(X36), c34), f11(f4(c32), c34)) | (~p25(X36, c36)))) | p2(f11(f4(c33), c34), f11(f4(c32), c34)) | (~p25(c32, c33)) | (~p25(c33, c36))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.11/0.39 tff(69,plain,
% 0.11/0.39 (p2(f11(f4(c33), c34), f11(f4(c32), c34))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[68, 62, 59, 56])).
% 0.11/0.39 tff(70,plain,
% 0.11/0.39 (^[X30: $i, X29: $i, X28: $i] : refl(((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30)) <=> ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(71,plain,
% 0.11/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30)) <=> ![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[70])).
% 0.11/0.39 tff(72,plain,
% 0.11/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30)) <=> ![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(73,plain,
% 0.11/0.39 (^[X30: $i, X29: $i, X28: $i] : trans(monotonicity(rewrite((p2(X29, X30) | (~p2(X28, X29))) <=> ((~p2(X28, X29)) | p2(X29, X30))), (((p2(X29, X30) | (~p2(X28, X29))) | (~p2(X28, X30))) <=> (((~p2(X28, X29)) | p2(X29, X30)) | (~p2(X28, X30))))), rewrite((((~p2(X28, X29)) | p2(X29, X30)) | (~p2(X28, X30))) <=> ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))), (((p2(X29, X30) | (~p2(X28, X29))) | (~p2(X28, X30))) <=> ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(74,plain,
% 0.11/0.39 (![X30: $i, X29: $i, X28: $i] : ((p2(X29, X30) | (~p2(X28, X29))) | (~p2(X28, X30))) <=> ![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.11/0.39 tff(75,axiom,(![X30: $i, X29: $i, X28: $i] : ((p2(X29, X30) | (~p2(X28, X29))) | (~p2(X28, X30)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_31')).
% 0.11/0.39 tff(76,plain,
% 0.11/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.11/0.39 tff(77,plain,
% 0.11/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.11/0.39 tff(78,plain,(
% 0.11/0.39 ![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.11/0.39 inference(skolemize,[status(sab)],[77])).
% 0.11/0.39 tff(79,plain,
% 0.11/0.39 (![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.11/0.39 tff(80,plain,
% 0.11/0.39 (((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | ((~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34))) | p2(f11(f4(c32), c34), f11(f4(c33), c34)))) <=> ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34))) | p2(f11(f4(c32), c34), f11(f4(c33), c34)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(81,plain,
% 0.11/0.39 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | ((~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34))) | p2(f11(f4(c32), c34), f11(f4(c33), c34)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(82,plain,
% 0.11/0.39 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | (~p2(f11(f4(c33), c34), f11(f4(c32), c34))) | (~p2(f11(f4(c33), c34), f11(f4(c33), c34))) | p2(f11(f4(c32), c34), f11(f4(c33), c34))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.11/0.39 tff(83,plain,
% 0.11/0.39 (p2(f11(f4(c32), c34), f11(f4(c33), c34))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[82, 79, 69, 46])).
% 0.11/0.39 tff(84,plain,
% 0.11/0.39 (^[X96: $i] : refl((~p2(X96, f16(X96, f9(f17(c31))))) <=> (~p2(X96, f16(X96, f9(f17(c31))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(85,plain,
% 0.11/0.39 (![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31))))) <=> ![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[84])).
% 0.11/0.39 tff(86,plain,
% 0.11/0.39 (![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31))))) <=> ![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(87,axiom,(![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p2_19')).
% 0.11/0.39 tff(88,plain,
% 0.11/0.39 (![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.11/0.39 tff(89,plain,(
% 0.11/0.39 ![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[88])).
% 0.11/0.39 tff(90,plain,
% 0.11/0.39 (![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.11/0.39 tff(91,plain,
% 0.11/0.39 ((~![X96: $i] : (~p2(X96, f16(X96, f9(f17(c31)))))) | (~p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(92,plain,
% 0.11/0.39 (~p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31))))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.11/0.39 tff(93,plain,
% 0.11/0.39 (p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31)))) <=> p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(94,axiom,(p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_39')).
% 0.11/0.39 tff(95,plain,
% 0.11/0.39 (p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.11/0.39 tff(96,plain,
% 0.11/0.39 (((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | ((~p2(f11(f4(c32), c34), f11(f4(c33), c34))) | (~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))))) <=> ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34))) | (~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(97,plain,
% 0.11/0.40 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | ((~p2(f11(f4(c32), c34), f11(f4(c33), c34))) | (~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31)))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(98,plain,
% 0.11/0.40 ((~![X30: $i, X29: $i, X28: $i] : ((~p2(X28, X29)) | (~p2(X28, X30)) | p2(X29, X30))) | (~p2(f11(f4(c32), c34), f11(f4(c33), c34))) | (~p2(f11(f4(c32), c34), f16(f11(f4(c33), c34), f9(f17(c31))))) | p2(f11(f4(c33), c34), f16(f11(f4(c33), c34), f9(f17(c31))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.11/0.40 tff(99,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[98, 79, 95, 92, 83])).
% 0.11/0.40 % SZS output end Proof
% 0.11/0.40 % E exiting
%------------------------------------------------------------------------------