TSTP Solution File: SYN673-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN673-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 : Thu Sep 29 23:56:53 EDT 2022
% Result : Unsatisfiable 0.18s 0.48s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYN673-1 : TPTP v8.1.0. Released v2.5.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 06:31:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.48 % SZS status Unsatisfiable
% 0.18/0.48 % SZS output start Proof
% 0.18/0.48 tff(p10_type, type, (
% 0.18/0.48 p10: ( $i * $i ) > $o)).
% 0.18/0.48 tff(c38_type, type, (
% 0.18/0.48 c38: $i)).
% 0.18/0.48 tff(f14_type, type, (
% 0.18/0.48 f14: ( $i * $i ) > $i)).
% 0.18/0.48 tff(f17_type, type, (
% 0.18/0.48 f17: ( $i * $i ) > $i)).
% 0.18/0.48 tff(c40_type, type, (
% 0.18/0.48 c40: $i)).
% 0.18/0.48 tff(c36_type, type, (
% 0.18/0.48 c36: $i)).
% 0.18/0.48 tff(f19_type, type, (
% 0.18/0.48 f19: ( $i * $i ) > $i)).
% 0.18/0.48 tff(c39_type, type, (
% 0.18/0.48 c39: $i)).
% 0.18/0.48 tff(c37_type, type, (
% 0.18/0.48 c37: $i)).
% 0.18/0.48 tff(c35_type, type, (
% 0.18/0.48 c35: $i)).
% 0.18/0.48 tff(p4_type, type, (
% 0.18/0.48 p4: ( $i * $i ) > $o)).
% 0.18/0.48 tff(f5_type, type, (
% 0.18/0.48 f5: ( $i * $i ) > $i)).
% 0.18/0.48 tff(f8_type, type, (
% 0.18/0.48 f8: ( $i * $i ) > $i)).
% 0.18/0.48 tff(c30_type, type, (
% 0.18/0.48 c30: $i)).
% 0.18/0.48 tff(c34_type, type, (
% 0.18/0.48 c34: $i)).
% 0.18/0.48 tff(c33_type, type, (
% 0.18/0.48 c33: $i)).
% 0.18/0.48 tff(p29_type, type, (
% 0.18/0.48 p29: ( $i * $i ) > $o)).
% 0.18/0.48 tff(p27_type, type, (
% 0.18/0.48 p27: ( $i * $i ) > $o)).
% 0.18/0.48 tff(f12_type, type, (
% 0.18/0.48 f12: ( $i * $i ) > $i)).
% 0.18/0.48 tff(c32_type, type, (
% 0.18/0.48 c32: $i)).
% 0.18/0.48 tff(p28_type, type, (
% 0.18/0.48 p28: ( $i * $i ) > $o)).
% 0.18/0.48 tff(c31_type, type, (
% 0.18/0.48 c31: $i)).
% 0.18/0.48 tff(f21_type, type, (
% 0.18/0.48 f21: ( $i * $i ) > $i)).
% 0.18/0.48 tff(f26_type, type, (
% 0.18/0.48 f26: ( $i * $i ) > $i)).
% 0.18/0.48 tff(c43_type, type, (
% 0.18/0.48 c43: $i)).
% 0.18/0.48 tff(c41_type, type, (
% 0.18/0.48 c41: $i)).
% 0.18/0.48 tff(f24_type, type, (
% 0.18/0.48 f24: ( $i * $i ) > $i)).
% 0.18/0.48 tff(c42_type, type, (
% 0.18/0.48 c42: $i)).
% 0.18/0.48 tff(p16_type, type, (
% 0.18/0.48 p16: ( $i * $i ) > $o)).
% 0.18/0.48 tff(1,plain,
% 0.18/0.48 (^[X0: $i] : refl(p10(X0, X0) <=> p10(X0, X0))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(2,plain,
% 0.18/0.48 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.18/0.48 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.48 tff(3,plain,
% 0.18/0.48 (![X0: $i] : p10(X0, X0) <=> ![X0: $i] : p10(X0, X0)),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(4,axiom,(![X0: $i] : p10(X0, X0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_1')).
% 0.18/0.48 tff(5,plain,
% 0.18/0.48 (![X0: $i] : p10(X0, X0)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.18/0.48 tff(6,plain,(
% 0.18/0.48 ![X0: $i] : p10(X0, X0)),
% 0.18/0.48 inference(skolemize,[status(sab)],[5])).
% 0.18/0.48 tff(7,plain,
% 0.18/0.48 (![X0: $i] : p10(X0, X0)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.18/0.48 tff(8,plain,
% 0.18/0.48 ((~![X0: $i] : p10(X0, X0)) | p10(c38, c38)),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(9,plain,
% 0.18/0.48 (p10(c38, c38)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.18/0.48 tff(10,plain,
% 0.18/0.48 (p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))) <=> p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(11,axiom,(p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_41')).
% 0.18/0.48 tff(12,plain,
% 0.18/0.48 (p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.18/0.48 tff(13,plain,
% 0.18/0.48 (^[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)))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(14,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.48 tff(15,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(16,plain,
% 0.18/0.48 (^[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))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(17,plain,
% 0.18/0.48 (![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))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.48 tff(18,axiom,(![X0: $i, X2: $i, X1: $i] : ((p10(X1, X2) | (~p10(X0, X1))) | (~p10(X0, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_22')).
% 0.18/0.48 tff(19,plain,
% 0.18/0.48 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.48 tff(20,plain,
% 0.18/0.48 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.48 tff(21,plain,(
% 0.18/0.48 ![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.18/0.48 inference(skolemize,[status(sab)],[20])).
% 0.18/0.48 tff(22,plain,
% 0.18/0.48 (![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.18/0.48 tff(23,plain,
% 0.18/0.48 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(c38, c38)) | (~p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(c38, c38)) | (~p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(24,plain,
% 0.18/0.48 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(c38, c38)) | (~p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(25,plain,
% 0.18/0.48 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(c38, c38)) | (~p10(c38, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.48 tff(26,plain,
% 0.18/0.48 (p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[25, 22, 12, 9])).
% 0.18/0.48 tff(27,plain,
% 0.18/0.48 (^[X81: $i] : refl(p4(X81, X81) <=> p4(X81, X81))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(28,plain,
% 0.18/0.48 (![X81: $i] : p4(X81, X81) <=> ![X81: $i] : p4(X81, X81)),
% 0.18/0.48 inference(quant_intro,[status(thm)],[27])).
% 0.18/0.48 tff(29,plain,
% 0.18/0.48 (![X81: $i] : p4(X81, X81) <=> ![X81: $i] : p4(X81, X81)),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(30,axiom,(![X81: $i] : p4(X81, X81)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_5')).
% 0.18/0.48 tff(31,plain,
% 0.18/0.48 (![X81: $i] : p4(X81, X81)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.18/0.48 tff(32,plain,(
% 0.18/0.48 ![X81: $i] : p4(X81, X81)),
% 0.18/0.48 inference(skolemize,[status(sab)],[31])).
% 0.18/0.48 tff(33,plain,
% 0.18/0.48 (![X81: $i] : p4(X81, X81)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.18/0.48 tff(34,plain,
% 0.18/0.48 ((~![X81: $i] : p4(X81, X81)) | p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(35,plain,
% 0.18/0.48 (p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.18/0.48 tff(36,assumption,(~p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39))), introduced(assumption)).
% 0.18/0.48 tff(37,plain,
% 0.18/0.48 (^[X7: $i] : refl(p10(f14(f19(c35, X7), c41), X7) <=> p10(f14(f19(c35, X7), c41), X7))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(38,plain,
% 0.18/0.48 (![X7: $i] : p10(f14(f19(c35, X7), c41), X7) <=> ![X7: $i] : p10(f14(f19(c35, X7), c41), X7)),
% 0.18/0.48 inference(quant_intro,[status(thm)],[37])).
% 0.18/0.48 tff(39,plain,
% 0.18/0.48 (![X7: $i] : p10(f14(f19(c35, X7), c41), X7) <=> ![X7: $i] : p10(f14(f19(c35, X7), c41), X7)),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(40,axiom,(![X7: $i] : p10(f14(f19(c35, X7), c41), X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p10_16')).
% 0.18/0.48 tff(41,plain,
% 0.18/0.48 (![X7: $i] : p10(f14(f19(c35, X7), c41), X7)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.48 tff(42,plain,(
% 0.18/0.48 ![X7: $i] : p10(f14(f19(c35, X7), c41), X7)),
% 0.18/0.48 inference(skolemize,[status(sab)],[41])).
% 0.18/0.48 tff(43,plain,
% 0.18/0.48 (![X7: $i] : p10(f14(f19(c35, X7), c41), X7)),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.18/0.48 tff(44,plain,
% 0.18/0.48 ((~![X7: $i] : p10(f14(f19(c35, X7), c41), X7)) | p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(45,plain,
% 0.18/0.48 (p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.18/0.48 tff(46,plain,
% 0.18/0.48 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(47,plain,
% 0.18/0.48 (((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) <=> ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(48,plain,
% 0.18/0.48 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[47])).
% 0.18/0.48 tff(49,plain,
% 0.18/0.48 (((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)))),
% 0.18/0.48 inference(transitivity,[status(thm)],[48, 46])).
% 0.18/0.48 tff(50,plain,
% 0.18/0.48 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(51,plain,
% 0.18/0.48 ((~![X0: $i, X2: $i, X1: $i] : ((~p10(X0, X2)) | (~p10(X0, X1)) | p10(X1, X2))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), c41), f14(f19(c35, c37), c39))) | p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.18/0.48 tff(52,plain,
% 0.18/0.48 (p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[51, 22, 45])).
% 0.18/0.48 tff(53,plain,
% 0.18/0.48 (^[X73: $i] : refl(((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(54,plain,
% 0.18/0.48 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[53])).
% 0.18/0.48 tff(55,plain,
% 0.18/0.48 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(56,plain,
% 0.18/0.48 (^[X73: $i] : trans(monotonicity(rewrite((p29(f5(c33, f8(c34, c30)), X73) | (~p10(X73, f14(f19(c35, c37), c39)))) <=> ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73))), (((p29(f5(c33, f8(c34, c30)), X73) | (~p10(X73, f14(f19(c35, c37), c39)))) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> (((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73)) | (~p28(f21(c30, f26(c43, X73)), c31))))), rewrite((((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73)) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))), (((p29(f5(c33, f8(c34, c30)), X73) | (~p10(X73, f14(f19(c35, c37), c39)))) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(57,plain,
% 0.18/0.48 (![X73: $i] : ((p29(f5(c33, f8(c34, c30)), X73) | (~p10(X73, f14(f19(c35, c37), c39)))) | (~p28(f21(c30, f26(c43, X73)), c31))) <=> ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[56])).
% 0.18/0.48 tff(58,axiom,(![X73: $i] : ((p29(f5(c33, f8(c34, c30)), X73) | (~p10(X73, f14(f19(c35, c37), c39)))) | (~p28(f21(c30, f26(c43, X73)), c31)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p29_53')).
% 0.18/0.48 tff(59,plain,
% 0.18/0.48 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.18/0.48 tff(60,plain,
% 0.18/0.48 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.18/0.48 tff(61,plain,(
% 0.18/0.48 ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.18/0.48 inference(skolemize,[status(sab)],[60])).
% 0.18/0.48 tff(62,plain,
% 0.18/0.48 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.18/0.48 tff(63,plain,
% 0.18/0.48 (((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))) | ((~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | (~p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31)))) <=> ((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))) | (~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | (~p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31)))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(64,plain,
% 0.18/0.48 ((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))) | ((~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | (~p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(65,plain,
% 0.18/0.48 ((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | (~p28(f21(c30, f26(c43, X73)), c31)))) | (~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | (~p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.18/0.48 tff(66,plain,
% 0.18/0.48 (p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | (~p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[65, 62, 52])).
% 0.18/0.48 tff(67,plain,
% 0.18/0.48 (~p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31)),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[66, 36])).
% 0.18/0.48 tff(68,plain,
% 0.18/0.49 (^[X73: $i] : refl(((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39)) <=> ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39)))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(69,plain,
% 0.18/0.49 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39)) <=> ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.49 tff(70,plain,
% 0.18/0.49 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39)) <=> ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(71,plain,
% 0.18/0.49 (^[X73: $i] : rewrite(((p29(f24(c42, f26(c43, X73)), c39) | p29(f5(c33, f8(c34, c30)), X73)) | (~p10(X73, f14(f19(c35, c37), c39)))) <=> ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39)))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(72,plain,
% 0.18/0.49 (![X73: $i] : ((p29(f24(c42, f26(c43, X73)), c39) | p29(f5(c33, f8(c34, c30)), X73)) | (~p10(X73, f14(f19(c35, c37), c39)))) <=> ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[71])).
% 0.18/0.49 tff(73,axiom,(![X73: $i] : ((p29(f24(c42, f26(c43, X73)), c39) | p29(f5(c33, f8(c34, c30)), X73)) | (~p10(X73, f14(f19(c35, c37), c39))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p29_52')).
% 0.18/0.49 tff(74,plain,
% 0.18/0.49 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.49 tff(75,plain,
% 0.18/0.49 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.18/0.49 tff(76,plain,(
% 0.18/0.49 ![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.18/0.49 inference(skolemize,[status(sab)],[75])).
% 0.18/0.49 tff(77,plain,
% 0.18/0.49 (![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.18/0.49 tff(78,plain,
% 0.18/0.49 (((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))) | ((~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39))) <=> ((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))) | (~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(79,plain,
% 0.18/0.49 ((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))) | ((~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(80,plain,
% 0.18/0.49 ((~![X73: $i] : ((~p10(X73, f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), X73) | p29(f24(c42, f26(c43, X73)), c39))) | (~p10(f14(f19(c35, c37), c39), f14(f19(c35, c37), c39))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.18/0.49 tff(81,plain,
% 0.18/0.49 (p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)) | p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[80, 77, 52])).
% 0.18/0.49 tff(82,plain,
% 0.18/0.49 (p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[81, 36])).
% 0.18/0.49 tff(83,plain,
% 0.18/0.49 (^[X68: $i] : refl((p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39))) <=> (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(84,plain,
% 0.18/0.49 (![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39))) <=> ![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.49 tff(85,plain,
% 0.18/0.49 (![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39))) <=> ![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(86,axiom,(![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p28_37')).
% 0.18/0.49 tff(87,plain,
% 0.18/0.49 (![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.18/0.49 tff(88,plain,(
% 0.18/0.49 ![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))),
% 0.18/0.49 inference(skolemize,[status(sab)],[87])).
% 0.18/0.49 tff(89,plain,
% 0.18/0.49 (![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.18/0.49 tff(90,plain,
% 0.18/0.49 (((~![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))) | (p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31) | (~p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39)))) <=> ((~![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))) | p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31) | (~p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(91,plain,
% 0.18/0.49 ((~![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))) | (p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31) | (~p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39)))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(92,plain,
% 0.18/0.49 ((~![X68: $i] : (p28(f21(c30, X68), c31) | (~p29(f24(c42, X68), c39)))) | p28(f21(c30, f26(c43, f14(f19(c35, c37), c39))), c31) | (~p29(f24(c42, f26(c43, f14(f19(c35, c37), c39))), c39))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.18/0.49 tff(93,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[92, 89, 82, 67])).
% 0.18/0.49 tff(94,plain,(p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(95,plain,
% 0.18/0.49 (^[X59: $i, X60: $i] : refl((p27(f12(c32, X59), X60) | (~p29(X60, X59))) <=> (p27(f12(c32, X59), X60) | (~p29(X60, X59))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(96,plain,
% 0.18/0.49 (![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59))) <=> ![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[95])).
% 0.18/0.49 tff(97,plain,
% 0.18/0.49 (![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59))) <=> ![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(98,axiom,(![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p27_19')).
% 0.18/0.49 tff(99,plain,
% 0.18/0.49 (![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.49 tff(100,plain,(
% 0.18/0.49 ![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))),
% 0.18/0.49 inference(skolemize,[status(sab)],[99])).
% 0.18/0.49 tff(101,plain,
% 0.18/0.49 (![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.18/0.49 tff(102,plain,
% 0.18/0.49 (((~![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))) | (p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39))))) <=> ((~![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))) | p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(103,plain,
% 0.18/0.49 ((~![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))) | (p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(104,plain,
% 0.18/0.49 ((~![X59: $i, X60: $i] : (p27(f12(c32, X59), X60) | (~p29(X60, X59)))) | p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, c37), c39)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.18/0.49 tff(105,plain,
% 0.18/0.49 (p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[104, 101, 94])).
% 0.18/0.49 tff(106,assumption,(~p16(c40, c40)), introduced(assumption)).
% 0.18/0.49 tff(107,plain,
% 0.18/0.49 (^[X29: $i] : refl(p16(X29, X29) <=> p16(X29, X29))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(108,plain,
% 0.18/0.49 (![X29: $i] : p16(X29, X29) <=> ![X29: $i] : p16(X29, X29)),
% 0.18/0.49 inference(quant_intro,[status(thm)],[107])).
% 0.18/0.49 tff(109,plain,
% 0.18/0.49 (![X29: $i] : p16(X29, X29) <=> ![X29: $i] : p16(X29, X29)),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(110,axiom,(![X29: $i] : p16(X29, X29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p16_12')).
% 0.18/0.49 tff(111,plain,
% 0.18/0.49 (![X29: $i] : p16(X29, X29)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.18/0.49 tff(112,plain,(
% 0.18/0.49 ![X29: $i] : p16(X29, X29)),
% 0.18/0.49 inference(skolemize,[status(sab)],[111])).
% 0.18/0.49 tff(113,plain,
% 0.18/0.49 (![X29: $i] : p16(X29, X29)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.18/0.49 tff(114,plain,
% 0.18/0.49 ((~![X29: $i] : p16(X29, X29)) | p16(c40, c40)),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(115,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[114, 113, 106])).
% 0.18/0.49 tff(116,plain,(p16(c40, c40)), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(117,plain,
% 0.18/0.49 (^[X68: $i] : refl(((~p16(X68, c40)) | p28(f21(c30, X68), c31)) <=> ((~p16(X68, c40)) | p28(f21(c30, X68), c31)))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(118,plain,
% 0.18/0.49 (![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31)) <=> ![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[117])).
% 0.18/0.49 tff(119,plain,
% 0.18/0.49 (![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31)) <=> ![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(120,plain,
% 0.18/0.49 (^[X68: $i] : rewrite((p28(f21(c30, X68), c31) | (~p16(X68, c40))) <=> ((~p16(X68, c40)) | p28(f21(c30, X68), c31)))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(121,plain,
% 0.18/0.49 (![X68: $i] : (p28(f21(c30, X68), c31) | (~p16(X68, c40))) <=> ![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[120])).
% 0.18/0.49 tff(122,axiom,(![X68: $i] : (p28(f21(c30, X68), c31) | (~p16(X68, c40)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p28_20')).
% 0.18/0.49 tff(123,plain,
% 0.18/0.49 (![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.18/0.49 tff(124,plain,
% 0.18/0.49 (![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.18/0.49 tff(125,plain,(
% 0.18/0.49 ![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.18/0.49 inference(skolemize,[status(sab)],[124])).
% 0.18/0.49 tff(126,plain,
% 0.18/0.49 (![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.18/0.49 tff(127,plain,
% 0.18/0.49 (((~![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))) | ((~p16(c40, c40)) | p28(f21(c30, c40), c31))) <=> ((~![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))) | (~p16(c40, c40)) | p28(f21(c30, c40), c31))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(128,plain,
% 0.18/0.49 ((~![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))) | ((~p16(c40, c40)) | p28(f21(c30, c40), c31))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(129,plain,
% 0.18/0.49 ((~![X68: $i] : ((~p16(X68, c40)) | p28(f21(c30, X68), c31))) | (~p16(c40, c40)) | p28(f21(c30, c40), c31)),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.18/0.49 tff(130,plain,
% 0.18/0.49 (p28(f21(c30, c40), c31)),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[129, 126, 116])).
% 0.18/0.49 tff(131,plain,
% 0.18/0.49 (^[X62: $i, X61: $i] : refl(((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30)))) <=> ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(132,plain,
% 0.18/0.49 (![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30)))) <=> ![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[131])).
% 0.18/0.49 tff(133,plain,
% 0.18/0.49 (![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30)))) <=> ![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(134,plain,
% 0.18/0.49 (^[X62: $i, X61: $i] : trans(monotonicity(rewrite((p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))) | (~p28(f21(c30, X62), c31))) <=> ((~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))), (((p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))) | (~p28(f21(c30, X62), c31))) | (~p27(f12(c32, X61), f5(c33, f8(c34, c30))))) <=> (((~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30)))) | (~p27(f12(c32, X61), f5(c33, f8(c34, c30))))))), rewrite((((~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30)))) | (~p27(f12(c32, X61), f5(c33, f8(c34, c30))))) <=> ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))), (((p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))) | (~p28(f21(c30, X62), c31))) | (~p27(f12(c32, X61), f5(c33, f8(c34, c30))))) <=> ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(135,plain,
% 0.18/0.49 (![X62: $i, X61: $i] : ((p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))) | (~p28(f21(c30, X62), c31))) | (~p27(f12(c32, X61), f5(c33, f8(c34, c30))))) <=> ![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[134])).
% 0.18/0.49 tff(136,axiom,(![X62: $i, X61: $i] : ((p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))) | (~p28(f21(c30, X62), c31))) | (~p27(f12(c32, X61), f5(c33, f8(c34, c30)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p27_55')).
% 0.18/0.49 tff(137,plain,
% 0.18/0.49 (![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.18/0.49 tff(138,plain,
% 0.18/0.49 (![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.18/0.49 tff(139,plain,(
% 0.18/0.49 ![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.18/0.49 inference(skolemize,[status(sab)],[138])).
% 0.18/0.49 tff(140,plain,
% 0.18/0.49 (![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.18/0.49 tff(141,plain,
% 0.18/0.49 (((~![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))) | ((~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, c40), c31)) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30))))) <=> ((~![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))) | (~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, c40), c31)) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(142,plain,
% 0.18/0.49 ((~![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))) | ((~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, c40), c31)) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(143,plain,
% 0.18/0.49 ((~![X62: $i, X61: $i] : ((~p27(f12(c32, X61), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, X62), c31)) | p27(f12(c32, f14(f19(c35, X61), f17(c36, X62))), f5(c33, f8(c34, c30))))) | (~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, c40), c31)) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.18/0.49 tff(144,plain,
% 0.18/0.49 ((~p27(f12(c32, f14(f19(c35, c37), c39)), f5(c33, f8(c34, c30)))) | (~p28(f21(c30, c40), c31)) | p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[143, 140])).
% 0.18/0.49 tff(145,plain,
% 0.18/0.49 (p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[144, 130, 105])).
% 0.18/0.49 tff(146,plain,
% 0.18/0.49 (^[X59: $i, X60: $i] : refl(((~p27(f12(c32, X59), X60)) | p29(X60, X59)) <=> ((~p27(f12(c32, X59), X60)) | p29(X60, X59)))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(147,plain,
% 0.18/0.49 (![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59)) <=> ![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[146])).
% 0.18/0.49 tff(148,plain,
% 0.18/0.49 (![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59)) <=> ![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(149,plain,
% 0.18/0.49 (^[X59: $i, X60: $i] : rewrite((p29(X60, X59) | (~p27(f12(c32, X59), X60))) <=> ((~p27(f12(c32, X59), X60)) | p29(X60, X59)))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(150,plain,
% 0.18/0.49 (![X59: $i, X60: $i] : (p29(X60, X59) | (~p27(f12(c32, X59), X60))) <=> ![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[149])).
% 0.18/0.50 tff(151,axiom,(![X59: $i, X60: $i] : (p29(X60, X59) | (~p27(f12(c32, X59), X60)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p29_18')).
% 0.18/0.50 tff(152,plain,
% 0.18/0.50 (![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.18/0.50 tff(153,plain,
% 0.18/0.50 (![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.18/0.50 tff(154,plain,(
% 0.18/0.50 ![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.18/0.50 inference(skolemize,[status(sab)],[153])).
% 0.18/0.50 tff(155,plain,
% 0.18/0.50 (![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.18/0.50 tff(156,plain,
% 0.18/0.50 (((~![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))) | ((~p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))))) <=> ((~![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))) | (~p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(157,plain,
% 0.18/0.50 ((~![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))) | ((~p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(158,plain,
% 0.18/0.50 ((~![X59: $i, X60: $i] : ((~p27(f12(c32, X59), X60)) | p29(X60, X59))) | (~p27(f12(c32, f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))), f5(c33, f8(c34, c30)))) | p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.18/0.50 tff(159,plain,
% 0.18/0.50 (p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[158, 155, 145])).
% 0.18/0.50 tff(160,plain,
% 0.18/0.50 (^[X72: $i, X70: $i, X69: $i, X71: $i] : refl(((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)) <=> ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(161,plain,
% 0.18/0.50 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)) <=> ![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[160])).
% 0.18/0.50 tff(162,plain,
% 0.18/0.50 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)) <=> ![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(163,plain,
% 0.18/0.50 (^[X72: $i, X70: $i, X69: $i, X71: $i] : trans(monotonicity(trans(monotonicity(rewrite((p29(X69, X70) | (~p29(X72, X71))) <=> ((~p29(X72, X71)) | p29(X69, X70))), (((p29(X69, X70) | (~p29(X72, X71))) | (~p4(X72, X69))) <=> (((~p29(X72, X71)) | p29(X69, X70)) | (~p4(X72, X69))))), rewrite((((~p29(X72, X71)) | p29(X69, X70)) | (~p4(X72, X69))) <=> ((~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))), (((p29(X69, X70) | (~p29(X72, X71))) | (~p4(X72, X69))) <=> ((~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)))), ((((p29(X69, X70) | (~p29(X72, X71))) | (~p4(X72, X69))) | (~p10(X71, X70))) <=> (((~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)) | (~p10(X71, X70))))), rewrite((((~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70)) | (~p10(X71, X70))) <=> ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))), ((((p29(X69, X70) | (~p29(X72, X71))) | (~p4(X72, X69))) | (~p10(X71, X70))) <=> ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(164,plain,
% 0.18/0.50 (![X72: $i, X70: $i, X69: $i, X71: $i] : (((p29(X69, X70) | (~p29(X72, X71))) | (~p4(X72, X69))) | (~p10(X71, X70))) <=> ![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[163])).
% 0.18/0.50 tff(165,axiom,(![X72: $i, X70: $i, X69: $i, X71: $i] : (((p29(X69, X70) | (~p29(X72, X71))) | (~p4(X72, X69))) | (~p10(X71, X70)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p29_38')).
% 0.18/0.50 tff(166,plain,
% 0.18/0.50 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.18/0.50 tff(167,plain,
% 0.18/0.50 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.18/0.50 tff(168,plain,(
% 0.18/0.50 ![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.18/0.50 inference(skolemize,[status(sab)],[167])).
% 0.18/0.50 tff(169,plain,
% 0.18/0.50 (![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.18/0.50 tff(170,plain,
% 0.18/0.50 ((~p29(f5(c33, f8(c34, c30)), c38)) <=> (~p29(f5(c33, f8(c34, c30)), c38))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(171,axiom,(~p29(f5(c33, f8(c34, c30)), c38)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p29_17')).
% 0.18/0.50 tff(172,plain,
% 0.18/0.50 (~p29(f5(c33, f8(c34, c30)), c38)),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.18/0.50 tff(173,plain,
% 0.18/0.50 (((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | (p29(f5(c33, f8(c34, c30)), c38) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))))) <=> ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | p29(f5(c33, f8(c34, c30)), c38) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(174,plain,
% 0.18/0.50 (((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p29(f5(c33, f8(c34, c30)), c38)) <=> (p29(f5(c33, f8(c34, c30)), c38) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(175,plain,
% 0.18/0.50 (((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p29(f5(c33, f8(c34, c30)), c38))) <=> ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | (p29(f5(c33, f8(c34, c30)), c38) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[174])).
% 0.18/0.50 tff(176,plain,
% 0.18/0.50 (((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p29(f5(c33, f8(c34, c30)), c38))) <=> ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | p29(f5(c33, f8(c34, c30)), c38) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[175, 173])).
% 0.18/0.50 tff(177,plain,
% 0.18/0.50 ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | ((~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)))) | p29(f5(c33, f8(c34, c30)), c38))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(178,plain,
% 0.18/0.50 ((~![X72: $i, X70: $i, X69: $i, X71: $i] : ((~p10(X71, X70)) | (~p4(X72, X69)) | (~p29(X72, X71)) | p29(X69, X70))) | p29(f5(c33, f8(c34, c30)), c38) | (~p4(f5(c33, f8(c34, c30)), f5(c33, f8(c34, c30)))) | (~p10(f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40)), c38)) | (~p29(f5(c33, f8(c34, c30)), f14(f19(c35, f14(f19(c35, c37), c39)), f17(c36, c40))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.18/0.50 tff(179,plain,
% 0.18/0.50 ($false),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[178, 172, 169, 159, 35, 26])).
% 0.18/0.50 % SZS output end Proof
%------------------------------------------------------------------------------