%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN659-1 : 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 05:39:47 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN659-1 : TPTP v9.0.0. Released v2.5.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 12:40:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% 0.20/0.38 tff(p14_type, type, (
% 0.20/0.38 p14: ( $i * $i ) > $o)).
% 0.20/0.38 tff(f15_type, type, (
% 0.20/0.38 f15: ( $i * $i ) > $i)).
% 0.20/0.38 tff(f13_type, type, (
% 0.20/0.38 f13: ( $i * $i ) > $i)).
% 0.20/0.38 tff(f17_type, type, (
% 0.20/0.38 f17: $i > $i)).
% 0.20/0.38 tff(c39_type, type, (
% 0.20/0.38 c39: $i)).
% 0.20/0.38 tff(f16_type, type, (
% 0.20/0.38 f16: $i > $i)).
% 0.20/0.38 tff(c29_type, type, (
% 0.20/0.38 c29: $i)).
% 0.20/0.38 tff(c41_type, type, (
% 0.20/0.38 c41: $i)).
% 0.20/0.38 tff(c40_type, type, (
% 0.20/0.38 c40: $i)).
% 0.20/0.38 tff(p12_type, type, (
% 0.20/0.38 p12: ( $i * $i ) > $o)).
% 0.20/0.38 tff(p7_type, type, (
% 0.20/0.38 p7: ( $i * $i ) > $o)).
% 0.20/0.38 tff(f8_type, type, (
% 0.20/0.38 f8: $i > $i)).
% 0.20/0.38 tff(c28_type, type, (
% 0.20/0.38 c28: $i)).
% 0.20/0.38 tff(c33_type, type, (
% 0.20/0.38 c33: $i)).
% 0.20/0.38 tff(c32_type, type, (
% 0.20/0.38 c32: $i)).
% 0.20/0.38 tff(p2_type, type, (
% 0.20/0.38 p2: ( $i * $i ) > $o)).
% 0.20/0.38 tff(c31_type, type, (
% 0.20/0.38 c31: $i)).
% 0.20/0.38 tff(p10_type, type, (
% 0.20/0.38 p10: ( $i * $i ) > $o)).
% 0.20/0.38 tff(p24_type, type, (
% 0.20/0.38 p24: ( $i * $i ) > $o)).
% 0.20/0.38 tff(1,assumption,(~p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))), introduced(assumption)).
% 0.20/0.38 tff(2,plain,
% 0.20/0.38 (^[X13: $i] : refl(p12(X13, X13) <=> p12(X13, X13))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(3,plain,
% 0.20/0.38 (![X13: $i] : p12(X13, X13) <=> ![X13: $i] : p12(X13, X13)),
% 0.20/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.38 tff(4,plain,
% 0.20/0.38 (![X13: $i] : p12(X13, X13) <=> ![X13: $i] : p12(X13, X13)),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(5,axiom,(![X13: $i] : p12(X13, X13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_10')).
% 0.20/0.38 tff(6,plain,
% 0.20/0.38 (![X13: $i] : p12(X13, X13)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.38 tff(7,plain,(
% 0.20/0.38 ![X13: $i] : p12(X13, X13)),
% 0.20/0.38 inference(skolemize,[status(sab)],[6])).
% 0.20/0.38 tff(8,plain,
% 0.20/0.38 (![X13: $i] : p12(X13, X13)),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.38 tff(9,plain,
% 0.20/0.38 ((~![X13: $i] : p12(X13, X13)) | p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))),
% 0.20/0.38 inference(quant_inst,[status(thm)],[])).
% 0.20/0.38 tff(10,plain,
% 0.20/0.38 ($false),
% 0.20/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.38 tff(11,plain,(p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.38 tff(12,plain,
% 0.20/0.38 (^[X87: $i, X88: $i, X89: $i] : refl(((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89)) <=> ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89)))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(13,plain,
% 0.20/0.38 (![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89)) <=> ![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.38 tff(14,plain,
% 0.20/0.38 (![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89)) <=> ![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))),
% 0.20/0.38 inference(rewrite,[status(thm)],[])).
% 0.20/0.38 tff(15,plain,
% 0.20/0.38 (^[X87: $i, X88: $i, X89: $i] : trans(monotonicity(rewrite((p7(X88, X89) | (~p7(X87, X88))) <=> ((~p7(X87, X88)) | p7(X88, X89))), (((p7(X88, X89) | (~p7(X87, X88))) | (~p7(X87, X89))) <=> (((~p7(X87, X88)) | p7(X88, X89)) | (~p7(X87, X89))))), rewrite((((~p7(X87, X88)) | p7(X88, X89)) | (~p7(X87, X89))) <=> ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))), (((p7(X88, X89) | (~p7(X87, X88))) | (~p7(X87, X89))) <=> ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))))),
% 0.20/0.38 inference(bind,[status(th)],[])).
% 0.20/0.38 tff(16,plain,
% 0.20/0.38 (![X87: $i, X88: $i, X89: $i] : ((p7(X88, X89) | (~p7(X87, X88))) | (~p7(X87, X89))) <=> ![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))),
% 0.20/0.38 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.38 tff(17,axiom,(![X87: $i, X88: $i, X89: $i] : ((p7(X88, X89) | (~p7(X87, X88))) | (~p7(X87, X89)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_31')).
% 0.20/0.38 tff(18,plain,
% 0.20/0.38 (![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.38 tff(19,plain,
% 0.20/0.38 (![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))),
% 0.20/0.38 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.38 tff(20,plain,(
% 0.20/0.38 ![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))),
% 0.20/0.38 inference(skolemize,[status(sab)],[19])).
% 0.20/0.39 tff(21,plain,
% 0.20/0.39 (![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (p7(f8(c28), c29) <=> p7(f8(c28), c29)),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(23,axiom,(p7(f8(c28), c29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_13')).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 (p7(f8(c28), c29)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (((~![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))) | ((~p7(f8(c28), c29)) | p7(c29, c29))) <=> ((~![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))) | (~p7(f8(c28), c29)) | p7(c29, c29))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (((~p7(f8(c28), c29)) | (~p7(f8(c28), c29)) | p7(c29, c29)) <=> ((~p7(f8(c28), c29)) | p7(c29, c29))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 (((~![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))) | ((~p7(f8(c28), c29)) | (~p7(f8(c28), c29)) | p7(c29, c29))) <=> ((~![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))) | ((~p7(f8(c28), c29)) | p7(c29, c29)))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[26])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 (((~![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))) | ((~p7(f8(c28), c29)) | (~p7(f8(c28), c29)) | p7(c29, c29))) <=> ((~![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))) | (~p7(f8(c28), c29)) | p7(c29, c29))),
% 0.20/0.39 inference(transitivity,[status(thm)],[27, 25])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 ((~![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))) | ((~p7(f8(c28), c29)) | (~p7(f8(c28), c29)) | p7(c29, c29))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 ((~![X87: $i, X88: $i, X89: $i] : ((~p7(X87, X89)) | (~p7(X87, X88)) | p7(X88, X89))) | (~p7(f8(c28), c29)) | p7(c29, c29)),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (p7(c29, c29)),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[30, 24, 21])).
% 0.20/0.39 tff(32,plain,
% 0.20/0.39 (^[X25: $i, X23: $i, X26: $i, X24: $i] : refl(((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26))) <=> ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(33,plain,
% 0.20/0.39 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26))) <=> ![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.39 tff(34,plain,
% 0.20/0.39 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26))) <=> ![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(35,plain,
% 0.20/0.39 (^[X25: $i, X23: $i, X26: $i, X24: $i] : trans(monotonicity(rewrite((p14(f15(X23, X24), f15(X25, X26)) | (~p12(X24, X26))) <=> ((~p12(X24, X26)) | p14(f15(X23, X24), f15(X25, X26)))), (((p14(f15(X23, X24), f15(X25, X26)) | (~p12(X24, X26))) | (~p7(X23, X25))) <=> (((~p12(X24, X26)) | p14(f15(X23, X24), f15(X25, X26))) | (~p7(X23, X25))))), rewrite((((~p12(X24, X26)) | p14(f15(X23, X24), f15(X25, X26))) | (~p7(X23, X25))) <=> ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))), (((p14(f15(X23, X24), f15(X25, X26)) | (~p12(X24, X26))) | (~p7(X23, X25))) <=> ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(36,plain,
% 0.20/0.39 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((p14(f15(X23, X24), f15(X25, X26)) | (~p12(X24, X26))) | (~p7(X23, X25))) <=> ![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.39 tff(37,axiom,(![X25: $i, X23: $i, X26: $i, X24: $i] : ((p14(f15(X23, X24), f15(X25, X26)) | (~p12(X24, X26))) | (~p7(X23, X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p14_45')).
% 0.20/0.39 tff(38,plain,
% 0.20/0.39 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.20/0.39 tff(39,plain,
% 0.20/0.39 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.20/0.39 tff(40,plain,(
% 0.20/0.39 ![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))),
% 0.20/0.39 inference(skolemize,[status(sab)],[39])).
% 0.20/0.39 tff(41,plain,
% 0.20/0.39 (![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.20/0.39 tff(42,plain,
% 0.20/0.39 (((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))) | ((~p7(c29, c29)) | (~p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))))) <=> ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))) | (~p7(c29, c29)) | (~p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(43,plain,
% 0.20/0.39 (((~p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))) | (~p7(c29, c29)) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))) <=> ((~p7(c29, c29)) | (~p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(44,plain,
% 0.20/0.39 (((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))) | ((~p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))) | (~p7(c29, c29)) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))))) <=> ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))) | ((~p7(c29, c29)) | (~p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[43])).
% 0.20/0.39 tff(45,plain,
% 0.20/0.39 (((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))) | ((~p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))) | (~p7(c29, c29)) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))))) <=> ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))) | (~p7(c29, c29)) | (~p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.39 tff(46,plain,
% 0.20/0.39 ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))) | ((~p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))) | (~p7(c29, c29)) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39)))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(47,plain,
% 0.20/0.39 ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))) | (~p7(c29, c29)) | (~p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.39 tff(48,plain,
% 0.20/0.39 ((~p12(f13(f16(c39), f17(c39)), f13(f16(c39), f17(c39)))) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[47, 41, 31])).
% 0.20/0.39 tff(49,plain,
% 0.20/0.39 (p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[48, 11])).
% 0.20/0.39 tff(50,plain,
% 0.20/0.39 (p12(f13(f16(c39), f17(c39)), f13(c40, c41)) <=> p12(f13(f16(c39), f17(c39)), f13(c40, c41))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(51,axiom,(p12(f13(f16(c39), f17(c39)), f13(c40, c41))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_29')).
% 0.20/0.39 tff(52,plain,
% 0.20/0.39 (p12(f13(f16(c39), f17(c39)), f13(c40, c41))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.39 tff(53,plain,
% 0.20/0.39 (((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))) | ((~p12(f13(f16(c39), f17(c39)), f13(c40, c41))) | (~p7(c29, c29)) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41))))) <=> ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))) | (~p12(f13(f16(c39), f17(c39)), f13(c40, c41))) | (~p7(c29, c29)) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(54,plain,
% 0.20/0.39 ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))) | ((~p12(f13(f16(c39), f17(c39)), f13(c40, c41))) | (~p7(c29, c29)) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(55,plain,
% 0.20/0.39 ((~![X25: $i, X23: $i, X26: $i, X24: $i] : ((~p12(X24, X26)) | (~p7(X23, X25)) | p14(f15(X23, X24), f15(X25, X26)))) | (~p12(f13(f16(c39), f17(c39)), f13(c40, c41))) | (~p7(c29, c29)) | p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41)))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.39 tff(56,plain,
% 0.20/0.39 (p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41)))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[55, 52, 41, 31])).
% 0.20/0.39 tff(57,plain,
% 0.20/0.39 (^[X22: $i, X21: $i, X20: $i] : refl(((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22)) <=> ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22)))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(58,plain,
% 0.20/0.39 (![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22)) <=> ![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.39 tff(59,plain,
% 0.20/0.39 (![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22)) <=> ![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(60,plain,
% 0.20/0.39 (^[X22: $i, X21: $i, X20: $i] : trans(monotonicity(rewrite((p14(X21, X22) | (~p14(X20, X21))) <=> ((~p14(X20, X21)) | p14(X21, X22))), (((p14(X21, X22) | (~p14(X20, X21))) | (~p14(X20, X22))) <=> (((~p14(X20, X21)) | p14(X21, X22)) | (~p14(X20, X22))))), rewrite((((~p14(X20, X21)) | p14(X21, X22)) | (~p14(X20, X22))) <=> ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))), (((p14(X21, X22) | (~p14(X20, X21))) | (~p14(X20, X22))) <=> ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(61,plain,
% 0.20/0.39 (![X22: $i, X21: $i, X20: $i] : ((p14(X21, X22) | (~p14(X20, X21))) | (~p14(X20, X22))) <=> ![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.39 tff(62,axiom,(![X22: $i, X21: $i, X20: $i] : ((p14(X21, X22) | (~p14(X20, X21))) | (~p14(X20, X22)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p14_37')).
% 0.20/0.39 tff(63,plain,
% 0.20/0.39 (![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.39 tff(64,plain,
% 0.20/0.39 (![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.39 tff(65,plain,(
% 0.20/0.39 ![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))),
% 0.20/0.39 inference(skolemize,[status(sab)],[64])).
% 0.20/0.39 tff(66,plain,
% 0.20/0.39 (![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 (((~![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))) | (p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41)))))) <=> ((~![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))) | p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 (((~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41)))) | p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39))))) <=> (p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 (((~![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))) | ((~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41)))) | p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))))) <=> ((~![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))) | (p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[68])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (((~![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))) | ((~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41)))) | p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))))) <=> ((~![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))) | p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[69, 67])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 ((~![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))) | ((~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41)))) | p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 ((~![X22: $i, X21: $i, X20: $i] : ((~p14(X20, X22)) | (~p14(X20, X21)) | p14(X21, X22))) | p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39)))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(f16(c39), f17(c39))))) | (~p14(f15(c29, f13(f16(c39), f17(c39))), f15(c29, f13(c40, c41))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[72, 66, 56, 49])).
% 0.20/0.40 tff(74,plain,
% 0.20/0.40 (^[X32: $i, X34: $i, X33: $i] : refl(((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34)) <=> ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(75,plain,
% 0.20/0.40 (![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34)) <=> ![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.40 tff(76,plain,
% 0.20/0.40 (![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34)) <=> ![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(77,plain,
% 0.20/0.40 (^[X32: $i, X34: $i, X33: $i] : trans(monotonicity(rewrite((p2(X33, X34) | (~p2(X32, X33))) <=> ((~p2(X32, X33)) | p2(X33, X34))), (((p2(X33, X34) | (~p2(X32, X33))) | (~p2(X32, X34))) <=> (((~p2(X32, X33)) | p2(X33, X34)) | (~p2(X32, X34))))), rewrite((((~p2(X32, X33)) | p2(X33, X34)) | (~p2(X32, X34))) <=> ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))), (((p2(X33, X34) | (~p2(X32, X33))) | (~p2(X32, X34))) <=> ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(78,plain,
% 0.20/0.40 (![X32: $i, X34: $i, X33: $i] : ((p2(X33, X34) | (~p2(X32, X33))) | (~p2(X32, X34))) <=> ![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[77])).
% 0.20/0.40 tff(79,axiom,(![X32: $i, X34: $i, X33: $i] : ((p2(X33, X34) | (~p2(X32, X33))) | (~p2(X32, X34)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_35')).
% 0.20/0.40 tff(80,plain,
% 0.20/0.40 (![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.20/0.40 tff(81,plain,
% 0.20/0.40 (![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.40 tff(82,plain,(
% 0.20/0.40 ![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))),
% 0.20/0.40 inference(skolemize,[status(sab)],[81])).
% 0.20/0.40 tff(83,plain,
% 0.20/0.40 (![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.20/0.40 tff(84,plain,
% 0.20/0.40 (p2(f17(c31), c33) <=> p2(f17(c31), c33)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(85,axiom,(p2(f17(c31), c33)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_15')).
% 0.20/0.40 tff(86,plain,
% 0.20/0.40 (p2(f17(c31), c33)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.40 tff(87,plain,
% 0.20/0.40 (((~![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))) | ((~p2(f17(c31), c33)) | p2(c33, c33))) <=> ((~![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))) | (~p2(f17(c31), c33)) | p2(c33, c33))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(88,plain,
% 0.20/0.40 (((~p2(f17(c31), c33)) | (~p2(f17(c31), c33)) | p2(c33, c33)) <=> ((~p2(f17(c31), c33)) | p2(c33, c33))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(89,plain,
% 0.20/0.40 (((~![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))) | ((~p2(f17(c31), c33)) | (~p2(f17(c31), c33)) | p2(c33, c33))) <=> ((~![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))) | ((~p2(f17(c31), c33)) | p2(c33, c33)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.40 tff(90,plain,
% 0.20/0.40 (((~![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))) | ((~p2(f17(c31), c33)) | (~p2(f17(c31), c33)) | p2(c33, c33))) <=> ((~![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))) | (~p2(f17(c31), c33)) | p2(c33, c33))),
% 0.20/0.40 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.40 tff(91,plain,
% 0.20/0.40 ((~![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))) | ((~p2(f17(c31), c33)) | (~p2(f17(c31), c33)) | p2(c33, c33))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(92,plain,
% 0.20/0.40 ((~![X32: $i, X34: $i, X33: $i] : ((~p2(X32, X34)) | (~p2(X32, X33)) | p2(X33, X34))) | (~p2(f17(c31), c33)) | p2(c33, c33)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.40 tff(93,plain,
% 0.20/0.40 (p2(c33, c33)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[92, 86, 83])).
% 0.20/0.40 tff(94,plain,
% 0.20/0.40 (^[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)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(95,plain,
% 0.20/0.40 (![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))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.40 tff(96,plain,
% 0.20/0.40 (![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))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(97,plain,
% 0.20/0.40 (^[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))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(98,plain,
% 0.20/0.40 (![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))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.40 tff(99,axiom,(![X0: $i, X2: $i, X1: $i] : ((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_30')).
% 0.20/0.40 tff(100,plain,
% 0.20/0.40 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.40 tff(101,plain,
% 0.20/0.40 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.20/0.40 tff(102,plain,(
% 0.20/0.40 ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.20/0.40 inference(skolemize,[status(sab)],[101])).
% 0.20/0.40 tff(103,plain,
% 0.20/0.40 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.20/0.40 tff(104,plain,
% 0.20/0.40 (p10(f16(c31), c32) <=> p10(f16(c31), c32)),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(105,axiom,(p10(f16(c31), c32)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_12')).
% 0.20/0.40 tff(106,plain,
% 0.20/0.40 (p10(f16(c31), c32)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.40 tff(107,plain,
% 0.20/0.40 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f16(c31), c32)) | p10(c32, c32))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(f16(c31), c32)) | p10(c32, c32))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(108,plain,
% 0.20/0.40 (((~p10(f16(c31), c32)) | (~p10(f16(c31), c32)) | p10(c32, c32)) <=> ((~p10(f16(c31), c32)) | p10(c32, c32))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(109,plain,
% 0.20/0.40 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f16(c31), c32)) | (~p10(f16(c31), c32)) | p10(c32, c32))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f16(c31), c32)) | p10(c32, c32)))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[108])).
% 0.20/0.40 tff(110,plain,
% 0.20/0.40 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f16(c31), c32)) | (~p10(f16(c31), c32)) | p10(c32, c32))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(f16(c31), c32)) | p10(c32, c32))),
% 0.20/0.40 inference(transitivity,[status(thm)],[109, 107])).
% 0.20/0.40 tff(111,plain,
% 0.20/0.40 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f16(c31), c32)) | (~p10(f16(c31), c32)) | p10(c32, c32))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(112,plain,
% 0.20/0.40 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(f16(c31), c32)) | p10(c32, c32)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.40 tff(113,plain,
% 0.20/0.40 (p10(c32, c32)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[112, 106, 103])).
% 0.20/0.40 tff(114,plain,
% 0.20/0.40 (^[X17: $i, X16: $i, X18: $i, X19: $i] : refl(((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19))) <=> ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(115,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19))) <=> ![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[114])).
% 0.20/0.40 tff(116,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19))) <=> ![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(117,plain,
% 0.20/0.40 (^[X17: $i, X16: $i, X18: $i, X19: $i] : trans(monotonicity(rewrite((p12(f13(X16, X17), f13(X18, X19)) | (~p10(X16, X18))) <=> ((~p10(X16, X18)) | p12(f13(X16, X17), f13(X18, X19)))), (((p12(f13(X16, X17), f13(X18, X19)) | (~p10(X16, X18))) | (~p2(X17, X19))) <=> (((~p10(X16, X18)) | p12(f13(X16, X17), f13(X18, X19))) | (~p2(X17, X19))))), rewrite((((~p10(X16, X18)) | p12(f13(X16, X17), f13(X18, X19))) | (~p2(X17, X19))) <=> ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))), (((p12(f13(X16, X17), f13(X18, X19)) | (~p10(X16, X18))) | (~p2(X17, X19))) <=> ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(118,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((p12(f13(X16, X17), f13(X18, X19)) | (~p10(X16, X18))) | (~p2(X17, X19))) <=> ![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.40 tff(119,axiom,(![X17: $i, X16: $i, X18: $i, X19: $i] : ((p12(f13(X16, X17), f13(X18, X19)) | (~p10(X16, X18))) | (~p2(X17, X19)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p12_44')).
% 0.20/0.40 tff(120,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.40 tff(121,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[120, 116])).
% 0.20/0.40 tff(122,plain,(
% 0.20/0.40 ![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))),
% 0.20/0.40 inference(skolemize,[status(sab)],[121])).
% 0.20/0.40 tff(123,plain,
% 0.20/0.40 (![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[122, 115])).
% 0.20/0.40 tff(124,plain,
% 0.20/0.40 (((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))) | ((~p10(c32, c32)) | (~p2(c33, c33)) | p12(f13(c32, c33), f13(c32, c33)))) <=> ((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))) | (~p10(c32, c32)) | (~p2(c33, c33)) | p12(f13(c32, c33), f13(c32, c33)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(125,plain,
% 0.20/0.40 ((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))) | ((~p10(c32, c32)) | (~p2(c33, c33)) | p12(f13(c32, c33), f13(c32, c33)))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(126,plain,
% 0.20/0.40 ((~![X17: $i, X16: $i, X18: $i, X19: $i] : ((~p10(X16, X18)) | (~p2(X17, X19)) | p12(f13(X16, X17), f13(X18, X19)))) | (~p10(c32, c32)) | (~p2(c33, c33)) | p12(f13(c32, c33), f13(c32, c33))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.20/0.40 tff(127,plain,
% 0.20/0.40 (p12(f13(c32, c33), f13(c32, c33))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[126, 123, 113, 93])).
% 0.20/0.40 tff(128,plain,
% 0.20/0.40 (^[X67: $i, X68: $i, X70: $i, X69: $i] : refl(((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68)) <=> ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(129,plain,
% 0.20/0.40 (![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68)) <=> ![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[128])).
% 0.20/0.40 tff(130,plain,
% 0.20/0.40 (![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68)) <=> ![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(131,plain,
% 0.20/0.41 (^[X67: $i, X68: $i, X70: $i, X69: $i] : trans(monotonicity(trans(monotonicity(rewrite((p24(X67, X68) | (~p14(X70, X67))) <=> ((~p14(X70, X67)) | p24(X67, X68))), (((p24(X67, X68) | (~p14(X70, X67))) | (~p24(X70, X69))) <=> (((~p14(X70, X67)) | p24(X67, X68)) | (~p24(X70, X69))))), rewrite((((~p14(X70, X67)) | p24(X67, X68)) | (~p24(X70, X69))) <=> ((~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))), (((p24(X67, X68) | (~p14(X70, X67))) | (~p24(X70, X69))) <=> ((~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68)))), ((((p24(X67, X68) | (~p14(X70, X67))) | (~p24(X70, X69))) | (~p12(X69, X68))) <=> (((~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68)) | (~p12(X69, X68))))), rewrite((((~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68)) | (~p12(X69, X68))) <=> ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))), ((((p24(X67, X68) | (~p14(X70, X67))) | (~p24(X70, X69))) | (~p12(X69, X68))) <=> ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(132,plain,
% 0.20/0.41 (![X67: $i, X68: $i, X70: $i, X69: $i] : (((p24(X67, X68) | (~p14(X70, X67))) | (~p24(X70, X69))) | (~p12(X69, X68))) <=> ![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.41 tff(133,axiom,(![X67: $i, X68: $i, X70: $i, X69: $i] : (((p24(X67, X68) | (~p14(X70, X67))) | (~p24(X70, X69))) | (~p12(X69, X68)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p24_41')).
% 0.20/0.41 tff(134,plain,
% 0.20/0.41 (![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.41 tff(135,plain,
% 0.20/0.41 (![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.20/0.41 tff(136,plain,(
% 0.20/0.41 ![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))),
% 0.20/0.41 inference(skolemize,[status(sab)],[135])).
% 0.20/0.41 tff(137,plain,
% 0.20/0.41 (![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.20/0.41 tff(138,plain,
% 0.20/0.41 ((~p24(f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))) <=> (~p24(f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(139,axiom,(~p24(f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p24_39')).
% 0.20/0.41 tff(140,plain,
% 0.20/0.41 (~p24(f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.41 tff(141,plain,
% 0.20/0.41 (p24(f15(c29, f13(c40, c41)), f13(c32, c33)) <=> p24(f15(c29, f13(c40, c41)), f13(c32, c33))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(142,axiom,(p24(f15(c29, f13(c40, c41)), f13(c32, c33))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p24_27')).
% 0.20/0.41 tff(143,plain,
% 0.20/0.41 (p24(f15(c29, f13(c40, c41)), f13(c32, c33))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.41 tff(144,plain,
% 0.20/0.41 (((~![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))) | ((~p12(f13(c32, c33), f13(c32, c33))) | (~p24(f15(c29, f13(c40, c41)), f13(c32, c33))) | (~p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39))))) | p24(f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33)))) <=> ((~![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))) | (~p12(f13(c32, c33), f13(c32, c33))) | (~p24(f15(c29, f13(c40, c41)), f13(c32, c33))) | (~p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39))))) | p24(f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(145,plain,
% 0.20/0.41 ((~![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))) | ((~p12(f13(c32, c33), f13(c32, c33))) | (~p24(f15(c29, f13(c40, c41)), f13(c32, c33))) | (~p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39))))) | p24(f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(146,plain,
% 0.20/0.41 ((~![X67: $i, X68: $i, X70: $i, X69: $i] : ((~p12(X69, X68)) | (~p24(X70, X69)) | (~p14(X70, X67)) | p24(X67, X68))) | (~p12(f13(c32, c33), f13(c32, c33))) | (~p24(f15(c29, f13(c40, c41)), f13(c32, c33))) | (~p14(f15(c29, f13(c40, c41)), f15(c29, f13(f16(c39), f17(c39))))) | p24(f15(c29, f13(f16(c39), f17(c39))), f13(c32, c33))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.41 tff(147,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[146, 143, 140, 137, 127, 73])).
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------