TSTP Solution File: SYN580-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN580-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 23:56:30 EDT 2022
% Result : Unsatisfiable 4.86s 3.38s
% Output : Proof 4.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN580-1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Sep 5 05:56:41 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 4.86/3.38 % SZS status Unsatisfiable
% 4.86/3.38 % SZS output start Proof
% 4.86/3.38 tff(p8_type, type, (
% 4.86/3.38 p8: ( $i * $i * $i ) > $o)).
% 4.86/3.38 tff(f3_type, type, (
% 4.86/3.38 f3: $i > $i)).
% 4.86/3.38 tff(c15_type, type, (
% 4.86/3.38 c15: $i)).
% 4.86/3.38 tff(f6_type, type, (
% 4.86/3.38 f6: $i > $i)).
% 4.86/3.38 tff(c14_type, type, (
% 4.86/3.38 c14: $i)).
% 4.86/3.38 tff(c12_type, type, (
% 4.86/3.38 c12: $i)).
% 4.86/3.38 tff(p9_type, type, (
% 4.86/3.38 p9: ( $i * $i ) > $o)).
% 4.86/3.38 tff(p4_type, type, (
% 4.86/3.38 p4: ( $i * $i ) > $o)).
% 4.86/3.38 tff(p2_type, type, (
% 4.86/3.38 p2: ( $i * $i ) > $o)).
% 4.86/3.38 tff(p7_type, type, (
% 4.86/3.38 p7: ( $i * $i ) > $o)).
% 4.86/3.38 tff(f5_type, type, (
% 4.86/3.38 f5: $i > $i)).
% 4.86/3.38 tff(c13_type, type, (
% 4.86/3.38 c13: $i)).
% 4.86/3.38 tff(p11_type, type, (
% 4.86/3.38 p11: ( $i * $i ) > $o)).
% 4.86/3.38 tff(c16_type, type, (
% 4.86/3.38 c16: $i)).
% 4.86/3.38 tff(1,assumption,(p8(c12, f6(f3(c15)), f3(c15))), introduced(assumption)).
% 4.86/3.38 tff(2,plain,
% 4.86/3.38 (^[X7: $i] : refl(p2(X7, X7) <=> p2(X7, X7))),
% 4.86/3.38 inference(bind,[status(th)],[])).
% 4.86/3.38 tff(3,plain,
% 4.86/3.38 (![X7: $i] : p2(X7, X7) <=> ![X7: $i] : p2(X7, X7)),
% 4.86/3.38 inference(quant_intro,[status(thm)],[2])).
% 4.86/3.38 tff(4,plain,
% 4.86/3.38 (![X7: $i] : p2(X7, X7) <=> ![X7: $i] : p2(X7, X7)),
% 4.86/3.38 inference(rewrite,[status(thm)],[])).
% 4.86/3.38 tff(5,axiom,(![X7: $i] : p2(X7, X7)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_4')).
% 4.86/3.38 tff(6,plain,
% 4.86/3.38 (![X7: $i] : p2(X7, X7)),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 4.86/3.38 tff(7,plain,(
% 4.86/3.38 ![X7: $i] : p2(X7, X7)),
% 4.86/3.38 inference(skolemize,[status(sab)],[6])).
% 4.86/3.38 tff(8,plain,
% 4.86/3.38 (![X7: $i] : p2(X7, X7)),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 4.86/3.38 tff(9,plain,
% 4.86/3.38 ((~![X7: $i] : p2(X7, X7)) | p2(c14, c14)),
% 4.86/3.38 inference(quant_inst,[status(thm)],[])).
% 4.86/3.38 tff(10,plain,
% 4.86/3.38 (p2(c14, c14)),
% 4.86/3.38 inference(unit_resolution,[status(thm)],[9, 8])).
% 4.86/3.38 tff(11,plain,
% 4.86/3.38 (^[X17: $i, X18: $i] : refl(((~p2(X17, X18)) | p4(f6(X17), f6(X18))) <=> ((~p2(X17, X18)) | p4(f6(X17), f6(X18))))),
% 4.86/3.38 inference(bind,[status(th)],[])).
% 4.86/3.38 tff(12,plain,
% 4.86/3.38 (![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18))) <=> ![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))),
% 4.86/3.38 inference(quant_intro,[status(thm)],[11])).
% 4.86/3.38 tff(13,plain,
% 4.86/3.38 (![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18))) <=> ![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))),
% 4.86/3.38 inference(rewrite,[status(thm)],[])).
% 4.86/3.38 tff(14,plain,
% 4.86/3.38 (^[X17: $i, X18: $i] : rewrite((p4(f6(X17), f6(X18)) | (~p2(X17, X18))) <=> ((~p2(X17, X18)) | p4(f6(X17), f6(X18))))),
% 4.86/3.38 inference(bind,[status(th)],[])).
% 4.86/3.38 tff(15,plain,
% 4.86/3.38 (![X17: $i, X18: $i] : (p4(f6(X17), f6(X18)) | (~p2(X17, X18))) <=> ![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))),
% 4.86/3.38 inference(quant_intro,[status(thm)],[14])).
% 4.86/3.38 tff(16,axiom,(![X17: $i, X18: $i] : (p4(f6(X17), f6(X18)) | (~p2(X17, X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_9')).
% 4.86/3.38 tff(17,plain,
% 4.86/3.38 (![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 4.86/3.38 tff(18,plain,
% 4.86/3.38 (![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 4.86/3.38 tff(19,plain,(
% 4.86/3.38 ![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))),
% 4.86/3.38 inference(skolemize,[status(sab)],[18])).
% 4.86/3.38 tff(20,plain,
% 4.86/3.38 (![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[19, 12])).
% 4.86/3.38 tff(21,plain,
% 4.86/3.38 (((~![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))) | ((~p2(c14, c14)) | p4(f6(c14), f6(c14)))) <=> ((~![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))) | (~p2(c14, c14)) | p4(f6(c14), f6(c14)))),
% 4.86/3.38 inference(rewrite,[status(thm)],[])).
% 4.86/3.38 tff(22,plain,
% 4.86/3.38 ((~![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))) | ((~p2(c14, c14)) | p4(f6(c14), f6(c14)))),
% 4.86/3.38 inference(quant_inst,[status(thm)],[])).
% 4.86/3.38 tff(23,plain,
% 4.86/3.38 ((~![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))) | (~p2(c14, c14)) | p4(f6(c14), f6(c14))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 4.86/3.38 tff(24,plain,
% 4.86/3.38 (p4(f6(c14), f6(c14))),
% 4.86/3.38 inference(unit_resolution,[status(thm)],[23, 20, 10])).
% 4.86/3.38 tff(25,plain,
% 4.86/3.38 (p2(c14, f3(c15)) <=> p2(c14, f3(c15))),
% 4.86/3.38 inference(rewrite,[status(thm)],[])).
% 4.86/3.38 tff(26,axiom,(p2(c14, f3(c15))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_7')).
% 4.86/3.38 tff(27,plain,
% 4.86/3.38 (p2(c14, f3(c15))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 4.86/3.38 tff(28,plain,
% 4.86/3.38 (((~![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))) | ((~p2(c14, f3(c15))) | p4(f6(c14), f6(f3(c15))))) <=> ((~![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))) | (~p2(c14, f3(c15))) | p4(f6(c14), f6(f3(c15))))),
% 4.86/3.38 inference(rewrite,[status(thm)],[])).
% 4.86/3.38 tff(29,plain,
% 4.86/3.38 ((~![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))) | ((~p2(c14, f3(c15))) | p4(f6(c14), f6(f3(c15))))),
% 4.86/3.38 inference(quant_inst,[status(thm)],[])).
% 4.86/3.38 tff(30,plain,
% 4.86/3.38 ((~![X17: $i, X18: $i] : ((~p2(X17, X18)) | p4(f6(X17), f6(X18)))) | (~p2(c14, f3(c15))) | p4(f6(c14), f6(f3(c15)))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[29, 28])).
% 4.86/3.38 tff(31,plain,
% 4.86/3.38 (p4(f6(c14), f6(f3(c15)))),
% 4.86/3.38 inference(unit_resolution,[status(thm)],[30, 27, 20])).
% 4.86/3.38 tff(32,plain,
% 4.86/3.38 (^[X14: $i, X12: $i, X13: $i] : refl(((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14)) <=> ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14)))),
% 4.86/3.38 inference(bind,[status(th)],[])).
% 4.86/3.38 tff(33,plain,
% 4.86/3.38 (![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14)) <=> ![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 4.86/3.38 inference(quant_intro,[status(thm)],[32])).
% 4.86/3.38 tff(34,plain,
% 4.86/3.38 (![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14)) <=> ![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 4.86/3.38 inference(rewrite,[status(thm)],[])).
% 4.86/3.38 tff(35,plain,
% 4.86/3.38 (^[X14: $i, X12: $i, X13: $i] : trans(monotonicity(rewrite((p4(X13, X14) | (~p4(X12, X13))) <=> ((~p4(X12, X13)) | p4(X13, X14))), (((p4(X13, X14) | (~p4(X12, X13))) | (~p4(X12, X14))) <=> (((~p4(X12, X13)) | p4(X13, X14)) | (~p4(X12, X14))))), rewrite((((~p4(X12, X13)) | p4(X13, X14)) | (~p4(X12, X14))) <=> ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))), (((p4(X13, X14) | (~p4(X12, X13))) | (~p4(X12, X14))) <=> ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))))),
% 4.86/3.38 inference(bind,[status(th)],[])).
% 4.86/3.38 tff(36,plain,
% 4.86/3.38 (![X14: $i, X12: $i, X13: $i] : ((p4(X13, X14) | (~p4(X12, X13))) | (~p4(X12, X14))) <=> ![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 4.86/3.38 inference(quant_intro,[status(thm)],[35])).
% 4.86/3.38 tff(37,axiom,(![X14: $i, X12: $i, X13: $i] : ((p4(X13, X14) | (~p4(X12, X13))) | (~p4(X12, X14)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p4_14')).
% 4.86/3.38 tff(38,plain,
% 4.86/3.38 (![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 4.86/3.38 tff(39,plain,
% 4.86/3.38 (![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 4.86/3.38 tff(40,plain,(
% 4.86/3.38 ![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 4.86/3.38 inference(skolemize,[status(sab)],[39])).
% 4.86/3.38 tff(41,plain,
% 4.86/3.38 (![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[40, 33])).
% 4.86/3.38 tff(42,plain,
% 4.86/3.38 (((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f6(c14), f6(c14))) | (~p4(f6(c14), f6(f3(c15)))) | p4(f6(f3(c15)), f6(c14)))) <=> ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | (~p4(f6(c14), f6(c14))) | (~p4(f6(c14), f6(f3(c15)))) | p4(f6(f3(c15)), f6(c14)))),
% 4.86/3.38 inference(rewrite,[status(thm)],[])).
% 4.86/3.38 tff(43,plain,
% 4.86/3.38 ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | ((~p4(f6(c14), f6(c14))) | (~p4(f6(c14), f6(f3(c15)))) | p4(f6(f3(c15)), f6(c14)))),
% 4.86/3.38 inference(quant_inst,[status(thm)],[])).
% 4.86/3.38 tff(44,plain,
% 4.86/3.38 ((~![X14: $i, X12: $i, X13: $i] : ((~p4(X12, X14)) | (~p4(X12, X13)) | p4(X13, X14))) | (~p4(f6(c14), f6(c14))) | (~p4(f6(c14), f6(f3(c15)))) | p4(f6(f3(c15)), f6(c14))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 4.86/3.38 tff(45,plain,
% 4.86/3.38 (p4(f6(f3(c15)), f6(c14))),
% 4.86/3.38 inference(unit_resolution,[status(thm)],[44, 41, 31, 24])).
% 4.86/3.38 tff(46,plain,
% 4.86/3.38 (^[X9: $i, X7: $i, X8: $i] : refl(((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9)) <=> ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9)))),
% 4.86/3.38 inference(bind,[status(th)],[])).
% 4.86/3.38 tff(47,plain,
% 4.86/3.38 (![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9)) <=> ![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))),
% 4.86/3.38 inference(quant_intro,[status(thm)],[46])).
% 4.86/3.38 tff(48,plain,
% 4.86/3.38 (![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9)) <=> ![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))),
% 4.86/3.38 inference(rewrite,[status(thm)],[])).
% 4.86/3.38 tff(49,plain,
% 4.86/3.38 (^[X9: $i, X7: $i, X8: $i] : trans(monotonicity(rewrite((p2(X8, X9) | (~p2(X7, X8))) <=> ((~p2(X7, X8)) | p2(X8, X9))), (((p2(X8, X9) | (~p2(X7, X8))) | (~p2(X7, X9))) <=> (((~p2(X7, X8)) | p2(X8, X9)) | (~p2(X7, X9))))), rewrite((((~p2(X7, X8)) | p2(X8, X9)) | (~p2(X7, X9))) <=> ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))), (((p2(X8, X9) | (~p2(X7, X8))) | (~p2(X7, X9))) <=> ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))))),
% 4.86/3.38 inference(bind,[status(th)],[])).
% 4.86/3.38 tff(50,plain,
% 4.86/3.38 (![X9: $i, X7: $i, X8: $i] : ((p2(X8, X9) | (~p2(X7, X8))) | (~p2(X7, X9))) <=> ![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))),
% 4.86/3.38 inference(quant_intro,[status(thm)],[49])).
% 4.86/3.38 tff(51,axiom,(![X9: $i, X7: $i, X8: $i] : ((p2(X8, X9) | (~p2(X7, X8))) | (~p2(X7, X9)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_15')).
% 4.86/3.38 tff(52,plain,
% 4.86/3.38 (![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[51, 50])).
% 4.86/3.38 tff(53,plain,
% 4.86/3.38 (![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[52, 48])).
% 4.86/3.38 tff(54,plain,(
% 4.86/3.38 ![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))),
% 4.86/3.38 inference(skolemize,[status(sab)],[53])).
% 4.86/3.38 tff(55,plain,
% 4.86/3.38 (![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[54, 47])).
% 4.86/3.38 tff(56,plain,
% 4.86/3.38 (((~![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))) | ((~p2(c14, f3(c15))) | (~p2(c14, c14)) | p2(f3(c15), c14))) <=> ((~![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))) | (~p2(c14, f3(c15))) | (~p2(c14, c14)) | p2(f3(c15), c14))),
% 4.86/3.38 inference(rewrite,[status(thm)],[])).
% 4.86/3.38 tff(57,plain,
% 4.86/3.38 ((~![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))) | ((~p2(c14, f3(c15))) | (~p2(c14, c14)) | p2(f3(c15), c14))),
% 4.86/3.38 inference(quant_inst,[status(thm)],[])).
% 4.86/3.38 tff(58,plain,
% 4.86/3.38 ((~![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))) | (~p2(c14, f3(c15))) | (~p2(c14, c14)) | p2(f3(c15), c14)),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 4.86/3.38 tff(59,plain,
% 4.86/3.38 (p2(f3(c15), c14)),
% 4.86/3.38 inference(unit_resolution,[status(thm)],[58, 27, 55, 10])).
% 4.86/3.38 tff(60,plain,
% 4.86/3.38 (^[X19: $i] : refl(p7(X19, X19) <=> p7(X19, X19))),
% 4.86/3.38 inference(bind,[status(th)],[])).
% 4.86/3.38 tff(61,plain,
% 4.86/3.38 (![X19: $i] : p7(X19, X19) <=> ![X19: $i] : p7(X19, X19)),
% 4.86/3.38 inference(quant_intro,[status(thm)],[60])).
% 4.86/3.38 tff(62,plain,
% 4.86/3.38 (![X19: $i] : p7(X19, X19) <=> ![X19: $i] : p7(X19, X19)),
% 4.86/3.38 inference(rewrite,[status(thm)],[])).
% 4.86/3.38 tff(63,axiom,(![X19: $i] : p7(X19, X19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p7_2')).
% 4.86/3.38 tff(64,plain,
% 4.86/3.38 (![X19: $i] : p7(X19, X19)),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 4.86/3.38 tff(65,plain,(
% 4.86/3.38 ![X19: $i] : p7(X19, X19)),
% 4.86/3.38 inference(skolemize,[status(sab)],[64])).
% 4.86/3.38 tff(66,plain,
% 4.86/3.38 (![X19: $i] : p7(X19, X19)),
% 4.86/3.38 inference(modus_ponens,[status(thm)],[65, 61])).
% 4.86/3.38 tff(67,plain,
% 4.86/3.38 ((~![X19: $i] : p7(X19, X19)) | p7(c12, c12)),
% 4.86/3.38 inference(quant_inst,[status(thm)],[])).
% 4.86/3.38 tff(68,plain,
% 4.86/3.38 (p7(c12, c12)),
% 4.86/3.38 inference(unit_resolution,[status(thm)],[67, 66])).
% 4.86/3.38 tff(69,plain,
% 4.86/3.38 (^[X31: $i, X30: $i] : refl(((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31))) <=> ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31))))),
% 4.86/3.39 inference(bind,[status(th)],[])).
% 4.86/3.39 tff(70,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31))) <=> ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))),
% 4.86/3.39 inference(quant_intro,[status(thm)],[69])).
% 4.86/3.39 tff(71,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31))) <=> ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))),
% 4.86/3.39 inference(rewrite,[status(thm)],[])).
% 4.86/3.39 tff(72,plain,
% 4.86/3.39 (^[X31: $i, X30: $i] : rewrite(((p9(c12, f5(X31)) | p8(c12, X30, X31)) | (~p9(c12, X30))) <=> ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31))))),
% 4.86/3.39 inference(bind,[status(th)],[])).
% 4.86/3.39 tff(73,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((p9(c12, f5(X31)) | p8(c12, X30, X31)) | (~p9(c12, X30))) <=> ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))),
% 4.86/3.39 inference(quant_intro,[status(thm)],[72])).
% 4.86/3.39 tff(74,axiom,(![X31: $i, X30: $i] : ((p9(c12, f5(X31)) | p8(c12, X30, X31)) | (~p9(c12, X30)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_17')).
% 4.86/3.39 tff(75,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 4.86/3.39 tff(76,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[75, 71])).
% 4.86/3.39 tff(77,plain,(
% 4.86/3.39 ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))),
% 4.86/3.39 inference(skolemize,[status(sab)],[76])).
% 4.86/3.39 tff(78,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[77, 70])).
% 4.86/3.39 tff(79,plain,
% 4.86/3.39 ((~p8(c12, c13, c14)) <=> (~p8(c12, c13, c14))),
% 4.86/3.39 inference(rewrite,[status(thm)],[])).
% 4.86/3.39 tff(80,axiom,(~p8(c12, c13, c14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p8_8')).
% 4.86/3.39 tff(81,plain,
% 4.86/3.39 (~p8(c12, c13, c14)),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[80, 79])).
% 4.86/3.39 tff(82,plain,
% 4.86/3.39 (p9(c12, c13) <=> p9(c12, c13)),
% 4.86/3.39 inference(rewrite,[status(thm)],[])).
% 4.86/3.39 tff(83,axiom,(p9(c12, c13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_6')).
% 4.86/3.39 tff(84,plain,
% 4.86/3.39 (p9(c12, c13)),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[83, 82])).
% 4.86/3.39 tff(85,plain,
% 4.86/3.39 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))) | (p8(c12, c13, c14) | (~p9(c12, c13)) | p9(c12, f5(c14)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))) | p8(c12, c13, c14) | (~p9(c12, c13)) | p9(c12, f5(c14)))),
% 4.86/3.39 inference(rewrite,[status(thm)],[])).
% 4.86/3.39 tff(86,plain,
% 4.86/3.39 (((~p9(c12, c13)) | p8(c12, c13, c14) | p9(c12, f5(c14))) <=> (p8(c12, c13, c14) | (~p9(c12, c13)) | p9(c12, f5(c14)))),
% 4.86/3.39 inference(rewrite,[status(thm)],[])).
% 4.86/3.39 tff(87,plain,
% 4.86/3.39 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))) | ((~p9(c12, c13)) | p8(c12, c13, c14) | p9(c12, f5(c14)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))) | (p8(c12, c13, c14) | (~p9(c12, c13)) | p9(c12, f5(c14))))),
% 4.86/3.39 inference(monotonicity,[status(thm)],[86])).
% 4.86/3.39 tff(88,plain,
% 4.86/3.39 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))) | ((~p9(c12, c13)) | p8(c12, c13, c14) | p9(c12, f5(c14)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))) | p8(c12, c13, c14) | (~p9(c12, c13)) | p9(c12, f5(c14)))),
% 4.86/3.39 inference(transitivity,[status(thm)],[87, 85])).
% 4.86/3.39 tff(89,plain,
% 4.86/3.39 ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))) | ((~p9(c12, c13)) | p8(c12, c13, c14) | p9(c12, f5(c14)))),
% 4.86/3.39 inference(quant_inst,[status(thm)],[])).
% 4.86/3.39 tff(90,plain,
% 4.86/3.39 ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | p9(c12, f5(X31)))) | p8(c12, c13, c14) | (~p9(c12, c13)) | p9(c12, f5(c14))),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[89, 88])).
% 4.86/3.39 tff(91,plain,
% 4.86/3.39 (p9(c12, f5(c14))),
% 4.86/3.39 inference(unit_resolution,[status(thm)],[90, 84, 81, 78])).
% 4.86/3.39 tff(92,plain,
% 4.86/3.39 (^[X31: $i, X30: $i] : refl(((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31)))) <=> ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31)))))),
% 4.86/3.39 inference(bind,[status(th)],[])).
% 4.86/3.39 tff(93,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31)))) <=> ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))),
% 4.86/3.39 inference(quant_intro,[status(thm)],[92])).
% 4.86/3.39 tff(94,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31)))) <=> ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))),
% 4.86/3.39 inference(rewrite,[status(thm)],[])).
% 4.86/3.39 tff(95,plain,
% 4.86/3.39 (^[X31: $i, X30: $i] : trans(monotonicity(rewrite((p8(c12, X30, X31) | (~p9(c12, X30))) <=> ((~p9(c12, X30)) | p8(c12, X30, X31))), (((p8(c12, X30, X31) | (~p9(c12, X30))) | (~p8(c12, f5(X31), f3(X31)))) <=> (((~p9(c12, X30)) | p8(c12, X30, X31)) | (~p8(c12, f5(X31), f3(X31)))))), rewrite((((~p9(c12, X30)) | p8(c12, X30, X31)) | (~p8(c12, f5(X31), f3(X31)))) <=> ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))), (((p8(c12, X30, X31) | (~p9(c12, X30))) | (~p8(c12, f5(X31), f3(X31)))) <=> ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))))),
% 4.86/3.39 inference(bind,[status(th)],[])).
% 4.86/3.39 tff(96,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((p8(c12, X30, X31) | (~p9(c12, X30))) | (~p8(c12, f5(X31), f3(X31)))) <=> ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))),
% 4.86/3.39 inference(quant_intro,[status(thm)],[95])).
% 4.86/3.39 tff(97,axiom,(![X31: $i, X30: $i] : ((p8(c12, X30, X31) | (~p9(c12, X30))) | (~p8(c12, f5(X31), f3(X31))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_21')).
% 4.86/3.39 tff(98,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[97, 96])).
% 4.86/3.39 tff(99,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[98, 94])).
% 4.86/3.39 tff(100,plain,(
% 4.86/3.39 ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))),
% 4.86/3.39 inference(skolemize,[status(sab)],[99])).
% 4.86/3.39 tff(101,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[100, 93])).
% 4.86/3.39 tff(102,plain,
% 4.86/3.39 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))) | (p8(c12, c13, c14) | (~p9(c12, c13)) | (~p8(c12, f5(c14), f3(c14))))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))) | p8(c12, c13, c14) | (~p9(c12, c13)) | (~p8(c12, f5(c14), f3(c14))))),
% 4.86/3.39 inference(rewrite,[status(thm)],[])).
% 4.86/3.39 tff(103,plain,
% 4.86/3.39 (((~p9(c12, c13)) | p8(c12, c13, c14) | (~p8(c12, f5(c14), f3(c14)))) <=> (p8(c12, c13, c14) | (~p9(c12, c13)) | (~p8(c12, f5(c14), f3(c14))))),
% 4.86/3.39 inference(rewrite,[status(thm)],[])).
% 4.86/3.39 tff(104,plain,
% 4.86/3.39 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))) | ((~p9(c12, c13)) | p8(c12, c13, c14) | (~p8(c12, f5(c14), f3(c14))))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))) | (p8(c12, c13, c14) | (~p9(c12, c13)) | (~p8(c12, f5(c14), f3(c14)))))),
% 4.86/3.39 inference(monotonicity,[status(thm)],[103])).
% 4.86/3.39 tff(105,plain,
% 4.86/3.39 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))) | ((~p9(c12, c13)) | p8(c12, c13, c14) | (~p8(c12, f5(c14), f3(c14))))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))) | p8(c12, c13, c14) | (~p9(c12, c13)) | (~p8(c12, f5(c14), f3(c14))))),
% 4.86/3.39 inference(transitivity,[status(thm)],[104, 102])).
% 4.86/3.39 tff(106,plain,
% 4.86/3.39 ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))) | ((~p9(c12, c13)) | p8(c12, c13, c14) | (~p8(c12, f5(c14), f3(c14))))),
% 4.86/3.39 inference(quant_inst,[status(thm)],[])).
% 4.86/3.39 tff(107,plain,
% 4.86/3.39 ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, X31) | (~p8(c12, f5(X31), f3(X31))))) | p8(c12, c13, c14) | (~p9(c12, c13)) | (~p8(c12, f5(c14), f3(c14)))),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[106, 105])).
% 4.86/3.39 tff(108,plain,
% 4.86/3.39 (~p8(c12, f5(c14), f3(c14))),
% 4.86/3.39 inference(unit_resolution,[status(thm)],[107, 84, 81, 101])).
% 4.86/3.39 tff(109,plain,
% 4.86/3.39 (^[X31: $i, X30: $i] : refl(((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31))) <=> ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31))))),
% 4.86/3.39 inference(bind,[status(th)],[])).
% 4.86/3.39 tff(110,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31))) <=> ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))),
% 4.86/3.39 inference(quant_intro,[status(thm)],[109])).
% 4.86/3.39 tff(111,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31))) <=> ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))),
% 4.86/3.39 inference(rewrite,[status(thm)],[])).
% 4.86/3.39 tff(112,plain,
% 4.86/3.39 (^[X31: $i, X30: $i] : trans(monotonicity(rewrite((p8(c12, X30, f3(X31)) | (~p9(c12, X30))) <=> ((~p9(c12, X30)) | p8(c12, X30, f3(X31)))), (((p8(c12, X30, f3(X31)) | (~p9(c12, X30))) | (~p8(c12, f6(X31), X31))) <=> (((~p9(c12, X30)) | p8(c12, X30, f3(X31))) | (~p8(c12, f6(X31), X31))))), rewrite((((~p9(c12, X30)) | p8(c12, X30, f3(X31))) | (~p8(c12, f6(X31), X31))) <=> ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))), (((p8(c12, X30, f3(X31)) | (~p9(c12, X30))) | (~p8(c12, f6(X31), X31))) <=> ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))))),
% 4.86/3.39 inference(bind,[status(th)],[])).
% 4.86/3.39 tff(113,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((p8(c12, X30, f3(X31)) | (~p9(c12, X30))) | (~p8(c12, f6(X31), X31))) <=> ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))),
% 4.86/3.39 inference(quant_intro,[status(thm)],[112])).
% 4.86/3.39 tff(114,axiom,(![X31: $i, X30: $i] : ((p8(c12, X30, f3(X31)) | (~p9(c12, X30))) | (~p8(c12, f6(X31), X31)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_22')).
% 4.86/3.39 tff(115,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[114, 113])).
% 4.86/3.39 tff(116,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[115, 111])).
% 4.86/3.39 tff(117,plain,(
% 4.86/3.39 ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))),
% 4.86/3.39 inference(skolemize,[status(sab)],[116])).
% 4.86/3.39 tff(118,plain,
% 4.86/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[117, 110])).
% 4.86/3.39 tff(119,plain,
% 4.86/3.39 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))) | (p8(c12, f5(c14), f3(c14)) | (~p9(c12, f5(c14))) | (~p8(c12, f6(c14), c14)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))) | p8(c12, f5(c14), f3(c14)) | (~p9(c12, f5(c14))) | (~p8(c12, f6(c14), c14)))),
% 4.86/3.39 inference(rewrite,[status(thm)],[])).
% 4.86/3.39 tff(120,plain,
% 4.86/3.39 (((~p9(c12, f5(c14))) | p8(c12, f5(c14), f3(c14)) | (~p8(c12, f6(c14), c14))) <=> (p8(c12, f5(c14), f3(c14)) | (~p9(c12, f5(c14))) | (~p8(c12, f6(c14), c14)))),
% 4.86/3.39 inference(rewrite,[status(thm)],[])).
% 4.86/3.39 tff(121,plain,
% 4.86/3.39 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))) | ((~p9(c12, f5(c14))) | p8(c12, f5(c14), f3(c14)) | (~p8(c12, f6(c14), c14)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))) | (p8(c12, f5(c14), f3(c14)) | (~p9(c12, f5(c14))) | (~p8(c12, f6(c14), c14))))),
% 4.86/3.39 inference(monotonicity,[status(thm)],[120])).
% 4.86/3.39 tff(122,plain,
% 4.86/3.39 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))) | ((~p9(c12, f5(c14))) | p8(c12, f5(c14), f3(c14)) | (~p8(c12, f6(c14), c14)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))) | p8(c12, f5(c14), f3(c14)) | (~p9(c12, f5(c14))) | (~p8(c12, f6(c14), c14)))),
% 4.86/3.39 inference(transitivity,[status(thm)],[121, 119])).
% 4.86/3.39 tff(123,plain,
% 4.86/3.39 ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))) | ((~p9(c12, f5(c14))) | p8(c12, f5(c14), f3(c14)) | (~p8(c12, f6(c14), c14)))),
% 4.86/3.39 inference(quant_inst,[status(thm)],[])).
% 4.86/3.39 tff(124,plain,
% 4.86/3.39 ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))) | p8(c12, f5(c14), f3(c14)) | (~p9(c12, f5(c14))) | (~p8(c12, f6(c14), c14))),
% 4.86/3.39 inference(modus_ponens,[status(thm)],[123, 122])).
% 4.86/3.39 tff(125,plain,
% 4.86/3.39 (~p8(c12, f6(c14), c14)),
% 4.86/3.39 inference(unit_resolution,[status(thm)],[124, 118, 108, 91])).
% 4.86/3.39 tff(126,plain,
% 4.86/3.39 (^[X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : refl(((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24)) <=> ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24)))),
% 4.86/3.39 inference(bind,[status(th)],[])).
% 4.86/3.39 tff(127,plain,
% 4.86/3.39 (![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24)) <=> ![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))),
% 4.86/3.39 inference(quant_intro,[status(thm)],[126])).
% 4.86/3.39 tff(128,plain,
% 4.86/3.39 (![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24)) <=> ![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))),
% 4.86/3.39 inference(rewrite,[status(thm)],[])).
% 4.86/3.39 tff(129,plain,
% 4.86/3.39 (^[X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((p8(X22, X23, X24) | (~p2(X25, X24))) <=> ((~p2(X25, X24)) | p8(X22, X23, X24))), (((p8(X22, X23, X24) | (~p2(X25, X24))) | (~p4(X26, X23))) <=> (((~p2(X25, X24)) | p8(X22, X23, X24)) | (~p4(X26, X23))))), rewrite((((~p2(X25, X24)) | p8(X22, X23, X24)) | (~p4(X26, X23))) <=> ((~p4(X26, X23)) | (~p2(X25, X24)) | p8(X22, X23, X24))), (((p8(X22, X23, X24) | (~p2(X25, X24))) | (~p4(X26, X23))) <=> ((~p4(X26, X23)) | (~p2(X25, X24)) | p8(X22, X23, X24)))), ((((p8(X22, X23, X24) | (~p2(X25, X24))) | (~p4(X26, X23))) | (~p7(X27, X22))) <=> (((~p4(X26, X23)) | (~p2(X25, X24)) | p8(X22, X23, X24)) | (~p7(X27, X22))))), rewrite((((~p4(X26, X23)) | (~p2(X25, X24)) | p8(X22, X23, X24)) | (~p7(X27, X22))) <=> ((~p4(X26, X23)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))), ((((p8(X22, X23, X24) | (~p2(X25, X24))) | (~p4(X26, X23))) | (~p7(X27, X22))) <=> ((~p4(X26, X23)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24)))), (((((p8(X22, X23, X24) | (~p2(X25, X24))) | (~p4(X26, X23))) | (~p7(X27, X22))) | (~p8(X27, X26, X25))) <=> (((~p4(X26, X23)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24)) | (~p8(X27, X26, X25))))), rewrite((((~p4(X26, X23)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24)) | (~p8(X27, X26, X25))) <=> ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))), (((((p8(X22, X23, X24) | (~p2(X25, X24))) | (~p4(X26, X23))) | (~p7(X27, X22))) | (~p8(X27, X26, X25))) <=> ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))))),
% 4.86/3.39 inference(bind,[status(th)],[])).
% 4.86/3.39 tff(130,plain,
% 4.86/3.39 (![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((((p8(X22, X23, X24) | (~p2(X25, X24))) | (~p4(X26, X23))) | (~p7(X27, X22))) | (~p8(X27, X26, X25))) <=> ![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))),
% 4.86/3.39 inference(quant_intro,[status(thm)],[129])).
% 4.89/3.39 tff(131,axiom,(![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((((p8(X22, X23, X24) | (~p2(X25, X24))) | (~p4(X26, X23))) | (~p7(X27, X22))) | (~p8(X27, X26, X25)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_23')).
% 4.89/3.39 tff(132,plain,
% 4.89/3.39 (![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))),
% 4.89/3.39 inference(modus_ponens,[status(thm)],[131, 130])).
% 4.89/3.39 tff(133,plain,
% 4.89/3.39 (![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))),
% 4.89/3.39 inference(modus_ponens,[status(thm)],[132, 128])).
% 4.89/3.39 tff(134,plain,(
% 4.89/3.39 ![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))),
% 4.89/3.39 inference(skolemize,[status(sab)],[133])).
% 4.89/3.39 tff(135,plain,
% 4.89/3.39 (![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))),
% 4.89/3.39 inference(modus_ponens,[status(thm)],[134, 127])).
% 4.89/3.39 tff(136,plain,
% 4.89/3.39 (((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | (p8(c12, f6(c14), c14) | (~p4(f6(f3(c15)), f6(c14))) | (~p2(f3(c15), c14)) | (~p7(c12, c12)) | (~p8(c12, f6(f3(c15)), f3(c15))))) <=> ((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | p8(c12, f6(c14), c14) | (~p4(f6(f3(c15)), f6(c14))) | (~p2(f3(c15), c14)) | (~p7(c12, c12)) | (~p8(c12, f6(f3(c15)), f3(c15))))),
% 4.89/3.39 inference(rewrite,[status(thm)],[])).
% 4.89/3.39 tff(137,plain,
% 4.89/3.39 (((~p4(f6(f3(c15)), f6(c14))) | (~p8(c12, f6(f3(c15)), f3(c15))) | (~p7(c12, c12)) | (~p2(f3(c15), c14)) | p8(c12, f6(c14), c14)) <=> (p8(c12, f6(c14), c14) | (~p4(f6(f3(c15)), f6(c14))) | (~p2(f3(c15), c14)) | (~p7(c12, c12)) | (~p8(c12, f6(f3(c15)), f3(c15))))),
% 4.89/3.39 inference(rewrite,[status(thm)],[])).
% 4.89/3.39 tff(138,plain,
% 4.89/3.39 (((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | ((~p4(f6(f3(c15)), f6(c14))) | (~p8(c12, f6(f3(c15)), f3(c15))) | (~p7(c12, c12)) | (~p2(f3(c15), c14)) | p8(c12, f6(c14), c14))) <=> ((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | (p8(c12, f6(c14), c14) | (~p4(f6(f3(c15)), f6(c14))) | (~p2(f3(c15), c14)) | (~p7(c12, c12)) | (~p8(c12, f6(f3(c15)), f3(c15)))))),
% 4.89/3.39 inference(monotonicity,[status(thm)],[137])).
% 4.89/3.39 tff(139,plain,
% 4.89/3.39 (((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | ((~p4(f6(f3(c15)), f6(c14))) | (~p8(c12, f6(f3(c15)), f3(c15))) | (~p7(c12, c12)) | (~p2(f3(c15), c14)) | p8(c12, f6(c14), c14))) <=> ((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | p8(c12, f6(c14), c14) | (~p4(f6(f3(c15)), f6(c14))) | (~p2(f3(c15), c14)) | (~p7(c12, c12)) | (~p8(c12, f6(f3(c15)), f3(c15))))),
% 4.89/3.39 inference(transitivity,[status(thm)],[138, 136])).
% 4.89/3.39 tff(140,plain,
% 4.89/3.39 ((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | ((~p4(f6(f3(c15)), f6(c14))) | (~p8(c12, f6(f3(c15)), f3(c15))) | (~p7(c12, c12)) | (~p2(f3(c15), c14)) | p8(c12, f6(c14), c14))),
% 4.89/3.39 inference(quant_inst,[status(thm)],[])).
% 4.89/3.39 tff(141,plain,
% 4.89/3.39 ((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | p8(c12, f6(c14), c14) | (~p4(f6(f3(c15)), f6(c14))) | (~p2(f3(c15), c14)) | (~p7(c12, c12)) | (~p8(c12, f6(f3(c15)), f3(c15)))),
% 4.89/3.39 inference(modus_ponens,[status(thm)],[140, 139])).
% 4.89/3.39 tff(142,plain,
% 4.89/3.39 ($false),
% 4.89/3.39 inference(unit_resolution,[status(thm)],[141, 135, 125, 68, 59, 45, 1])).
% 4.89/3.39 tff(143,plain,(~p8(c12, f6(f3(c15)), f3(c15))), inference(lemma,lemma(discharge,[]))).
% 4.89/3.39 tff(144,plain,
% 4.89/3.39 (^[X31: $i, X30: $i] : refl(((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31))) <=> ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31))))),
% 4.89/3.39 inference(bind,[status(th)],[])).
% 4.89/3.39 tff(145,plain,
% 4.89/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31))) <=> ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))),
% 4.89/3.39 inference(quant_intro,[status(thm)],[144])).
% 4.89/3.39 tff(146,plain,
% 4.89/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31))) <=> ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))),
% 4.89/3.39 inference(rewrite,[status(thm)],[])).
% 4.89/3.39 tff(147,plain,
% 4.89/3.39 (^[X31: $i, X30: $i] : rewrite(((p9(c12, f6(X31)) | p8(c12, X30, f3(X31))) | (~p9(c12, X30))) <=> ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31))))),
% 4.89/3.39 inference(bind,[status(th)],[])).
% 4.89/3.39 tff(148,plain,
% 4.89/3.39 (![X31: $i, X30: $i] : ((p9(c12, f6(X31)) | p8(c12, X30, f3(X31))) | (~p9(c12, X30))) <=> ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))),
% 4.89/3.39 inference(quant_intro,[status(thm)],[147])).
% 4.89/3.39 tff(149,axiom,(![X31: $i, X30: $i] : ((p9(c12, f6(X31)) | p8(c12, X30, f3(X31))) | (~p9(c12, X30)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_18')).
% 4.89/3.39 tff(150,plain,
% 4.89/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))),
% 4.89/3.39 inference(modus_ponens,[status(thm)],[149, 148])).
% 4.89/3.39 tff(151,plain,
% 4.89/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))),
% 4.89/3.39 inference(modus_ponens,[status(thm)],[150, 146])).
% 4.89/3.39 tff(152,plain,(
% 4.89/3.39 ![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))),
% 4.89/3.39 inference(skolemize,[status(sab)],[151])).
% 4.89/3.39 tff(153,plain,
% 4.89/3.39 (![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))),
% 4.89/3.39 inference(modus_ponens,[status(thm)],[152, 145])).
% 4.89/3.39 tff(154,plain,
% 4.89/3.39 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | (p8(c12, f5(c14), f3(c14)) | (~p9(c12, f5(c14))) | p9(c12, f6(c14)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | p8(c12, f5(c14), f3(c14)) | (~p9(c12, f5(c14))) | p9(c12, f6(c14)))),
% 4.89/3.39 inference(rewrite,[status(thm)],[])).
% 4.89/3.39 tff(155,plain,
% 4.89/3.39 (((~p9(c12, f5(c14))) | p8(c12, f5(c14), f3(c14)) | p9(c12, f6(c14))) <=> (p8(c12, f5(c14), f3(c14)) | (~p9(c12, f5(c14))) | p9(c12, f6(c14)))),
% 4.89/3.39 inference(rewrite,[status(thm)],[])).
% 4.89/3.39 tff(156,plain,
% 4.89/3.39 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | ((~p9(c12, f5(c14))) | p8(c12, f5(c14), f3(c14)) | p9(c12, f6(c14)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | (p8(c12, f5(c14), f3(c14)) | (~p9(c12, f5(c14))) | p9(c12, f6(c14))))),
% 4.89/3.39 inference(monotonicity,[status(thm)],[155])).
% 4.89/3.39 tff(157,plain,
% 4.89/3.39 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | ((~p9(c12, f5(c14))) | p8(c12, f5(c14), f3(c14)) | p9(c12, f6(c14)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | p8(c12, f5(c14), f3(c14)) | (~p9(c12, f5(c14))) | p9(c12, f6(c14)))),
% 4.89/3.39 inference(transitivity,[status(thm)],[156, 154])).
% 4.89/3.39 tff(158,plain,
% 4.89/3.39 ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | ((~p9(c12, f5(c14))) | p8(c12, f5(c14), f3(c14)) | p9(c12, f6(c14)))),
% 4.89/3.39 inference(quant_inst,[status(thm)],[])).
% 4.89/3.39 tff(159,plain,
% 4.89/3.39 ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | p8(c12, f5(c14), f3(c14)) | (~p9(c12, f5(c14))) | p9(c12, f6(c14))),
% 4.89/3.39 inference(modus_ponens,[status(thm)],[158, 157])).
% 4.89/3.40 tff(160,plain,
% 4.89/3.40 (p9(c12, f6(c14))),
% 4.89/3.40 inference(unit_resolution,[status(thm)],[159, 153, 108, 91])).
% 4.89/3.40 tff(161,plain,
% 4.89/3.40 (^[X32: $i, X35: $i, X34: $i, X33: $i] : refl(((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33)) <=> ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33)))),
% 4.89/3.40 inference(bind,[status(th)],[])).
% 4.89/3.40 tff(162,plain,
% 4.89/3.40 (![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33)) <=> ![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))),
% 4.89/3.40 inference(quant_intro,[status(thm)],[161])).
% 4.89/3.40 tff(163,plain,
% 4.89/3.40 (![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33)) <=> ![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(164,plain,
% 4.89/3.40 (^[X32: $i, X35: $i, X34: $i, X33: $i] : trans(monotonicity(trans(monotonicity(rewrite((p9(X32, X33) | (~p7(X35, X32))) <=> ((~p7(X35, X32)) | p9(X32, X33))), (((p9(X32, X33) | (~p7(X35, X32))) | (~p9(X35, X34))) <=> (((~p7(X35, X32)) | p9(X32, X33)) | (~p9(X35, X34))))), rewrite((((~p7(X35, X32)) | p9(X32, X33)) | (~p9(X35, X34))) <=> ((~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))), (((p9(X32, X33) | (~p7(X35, X32))) | (~p9(X35, X34))) <=> ((~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33)))), ((((p9(X32, X33) | (~p7(X35, X32))) | (~p9(X35, X34))) | (~p4(X34, X33))) <=> (((~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33)) | (~p4(X34, X33))))), rewrite((((~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33)) | (~p4(X34, X33))) <=> ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))), ((((p9(X32, X33) | (~p7(X35, X32))) | (~p9(X35, X34))) | (~p4(X34, X33))) <=> ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))))),
% 4.89/3.40 inference(bind,[status(th)],[])).
% 4.89/3.40 tff(165,plain,
% 4.89/3.40 (![X32: $i, X35: $i, X34: $i, X33: $i] : (((p9(X32, X33) | (~p7(X35, X32))) | (~p9(X35, X34))) | (~p4(X34, X33))) <=> ![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))),
% 4.89/3.40 inference(quant_intro,[status(thm)],[164])).
% 4.89/3.40 tff(166,axiom,(![X32: $i, X35: $i, X34: $i, X33: $i] : (((p9(X32, X33) | (~p7(X35, X32))) | (~p9(X35, X34))) | (~p4(X34, X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p9_19')).
% 4.89/3.40 tff(167,plain,
% 4.89/3.40 (![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[166, 165])).
% 4.89/3.40 tff(168,plain,
% 4.89/3.40 (![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[167, 163])).
% 4.89/3.40 tff(169,plain,(
% 4.89/3.40 ![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))),
% 4.89/3.40 inference(skolemize,[status(sab)],[168])).
% 4.89/3.40 tff(170,plain,
% 4.89/3.40 (![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[169, 162])).
% 4.89/3.40 tff(171,plain,
% 4.89/3.40 (((~![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))) | ((~p4(f6(c14), f6(f3(c15)))) | (~p7(c12, c12)) | (~p9(c12, f6(c14))) | p9(c12, f6(f3(c15))))) <=> ((~![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))) | (~p4(f6(c14), f6(f3(c15)))) | (~p7(c12, c12)) | (~p9(c12, f6(c14))) | p9(c12, f6(f3(c15))))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(172,plain,
% 4.89/3.40 (((~p4(f6(c14), f6(f3(c15)))) | (~p9(c12, f6(c14))) | (~p7(c12, c12)) | p9(c12, f6(f3(c15)))) <=> ((~p4(f6(c14), f6(f3(c15)))) | (~p7(c12, c12)) | (~p9(c12, f6(c14))) | p9(c12, f6(f3(c15))))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(173,plain,
% 4.89/3.40 (((~![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))) | ((~p4(f6(c14), f6(f3(c15)))) | (~p9(c12, f6(c14))) | (~p7(c12, c12)) | p9(c12, f6(f3(c15))))) <=> ((~![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))) | ((~p4(f6(c14), f6(f3(c15)))) | (~p7(c12, c12)) | (~p9(c12, f6(c14))) | p9(c12, f6(f3(c15)))))),
% 4.89/3.40 inference(monotonicity,[status(thm)],[172])).
% 4.89/3.40 tff(174,plain,
% 4.89/3.40 (((~![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))) | ((~p4(f6(c14), f6(f3(c15)))) | (~p9(c12, f6(c14))) | (~p7(c12, c12)) | p9(c12, f6(f3(c15))))) <=> ((~![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))) | (~p4(f6(c14), f6(f3(c15)))) | (~p7(c12, c12)) | (~p9(c12, f6(c14))) | p9(c12, f6(f3(c15))))),
% 4.89/3.40 inference(transitivity,[status(thm)],[173, 171])).
% 4.89/3.40 tff(175,plain,
% 4.89/3.40 ((~![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))) | ((~p4(f6(c14), f6(f3(c15)))) | (~p9(c12, f6(c14))) | (~p7(c12, c12)) | p9(c12, f6(f3(c15))))),
% 4.89/3.40 inference(quant_inst,[status(thm)],[])).
% 4.89/3.40 tff(176,plain,
% 4.89/3.40 ((~![X32: $i, X35: $i, X34: $i, X33: $i] : ((~p4(X34, X33)) | (~p9(X35, X34)) | (~p7(X35, X32)) | p9(X32, X33))) | (~p4(f6(c14), f6(f3(c15)))) | (~p7(c12, c12)) | (~p9(c12, f6(c14))) | p9(c12, f6(f3(c15)))),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[175, 174])).
% 4.89/3.40 tff(177,plain,
% 4.89/3.40 (p9(c12, f6(f3(c15)))),
% 4.89/3.40 inference(unit_resolution,[status(thm)],[176, 170, 31, 160, 68])).
% 4.89/3.40 tff(178,plain,
% 4.89/3.40 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | (p9(c12, f6(c15)) | (~p9(c12, f6(f3(c15)))) | p8(c12, f6(f3(c15)), f3(c15)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | p9(c12, f6(c15)) | (~p9(c12, f6(f3(c15)))) | p8(c12, f6(f3(c15)), f3(c15)))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(179,plain,
% 4.89/3.40 (((~p9(c12, f6(f3(c15)))) | p8(c12, f6(f3(c15)), f3(c15)) | p9(c12, f6(c15))) <=> (p9(c12, f6(c15)) | (~p9(c12, f6(f3(c15)))) | p8(c12, f6(f3(c15)), f3(c15)))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(180,plain,
% 4.89/3.40 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | ((~p9(c12, f6(f3(c15)))) | p8(c12, f6(f3(c15)), f3(c15)) | p9(c12, f6(c15)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | (p9(c12, f6(c15)) | (~p9(c12, f6(f3(c15)))) | p8(c12, f6(f3(c15)), f3(c15))))),
% 4.89/3.40 inference(monotonicity,[status(thm)],[179])).
% 4.89/3.40 tff(181,plain,
% 4.89/3.40 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | ((~p9(c12, f6(f3(c15)))) | p8(c12, f6(f3(c15)), f3(c15)) | p9(c12, f6(c15)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | p9(c12, f6(c15)) | (~p9(c12, f6(f3(c15)))) | p8(c12, f6(f3(c15)), f3(c15)))),
% 4.89/3.40 inference(transitivity,[status(thm)],[180, 178])).
% 4.89/3.40 tff(182,plain,
% 4.89/3.40 ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | ((~p9(c12, f6(f3(c15)))) | p8(c12, f6(f3(c15)), f3(c15)) | p9(c12, f6(c15)))),
% 4.89/3.40 inference(quant_inst,[status(thm)],[])).
% 4.89/3.40 tff(183,plain,
% 4.89/3.40 ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | p9(c12, f6(X31)))) | p9(c12, f6(c15)) | (~p9(c12, f6(f3(c15)))) | p8(c12, f6(f3(c15)), f3(c15))),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[182, 181])).
% 4.89/3.40 tff(184,plain,
% 4.89/3.40 (p9(c12, f6(c15)) | p8(c12, f6(f3(c15)), f3(c15))),
% 4.89/3.40 inference(unit_resolution,[status(thm)],[183, 153, 177])).
% 4.89/3.40 tff(185,plain,
% 4.89/3.40 (p9(c12, f6(c15))),
% 4.89/3.40 inference(unit_resolution,[status(thm)],[184, 143])).
% 4.89/3.40 tff(186,assumption,(~p8(c12, f6(c15), c15)), introduced(assumption)).
% 4.89/3.40 tff(187,assumption,(p9(c12, f6(c15))), introduced(assumption)).
% 4.89/3.40 tff(188,plain,
% 4.89/3.40 (^[X29: $i, X28: $i] : refl(((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29)) <=> ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29)))),
% 4.89/3.40 inference(bind,[status(th)],[])).
% 4.89/3.40 tff(189,plain,
% 4.89/3.40 (![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29)) <=> ![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))),
% 4.89/3.40 inference(quant_intro,[status(thm)],[188])).
% 4.89/3.40 tff(190,plain,
% 4.89/3.40 (![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29)) <=> ![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(191,plain,
% 4.89/3.40 (^[X29: $i, X28: $i] : trans(monotonicity(rewrite((p8(c12, X28, X29) | (~p11(X29, c16))) <=> ((~p11(X29, c16)) | p8(c12, X28, X29))), (((p8(c12, X28, X29) | (~p11(X29, c16))) | (~p9(c12, X28))) <=> (((~p11(X29, c16)) | p8(c12, X28, X29)) | (~p9(c12, X28))))), rewrite((((~p11(X29, c16)) | p8(c12, X28, X29)) | (~p9(c12, X28))) <=> ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))), (((p8(c12, X28, X29) | (~p11(X29, c16))) | (~p9(c12, X28))) <=> ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))))),
% 4.89/3.40 inference(bind,[status(th)],[])).
% 4.89/3.40 tff(192,plain,
% 4.89/3.40 (![X29: $i, X28: $i] : ((p8(c12, X28, X29) | (~p11(X29, c16))) | (~p9(c12, X28))) <=> ![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))),
% 4.89/3.40 inference(quant_intro,[status(thm)],[191])).
% 4.89/3.40 tff(193,axiom,(![X29: $i, X28: $i] : ((p8(c12, X28, X29) | (~p11(X29, c16))) | (~p9(c12, X28)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p8_16')).
% 4.89/3.40 tff(194,plain,
% 4.89/3.40 (![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[193, 192])).
% 4.89/3.40 tff(195,plain,
% 4.89/3.40 (![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[194, 190])).
% 4.89/3.40 tff(196,plain,(
% 4.89/3.40 ![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))),
% 4.89/3.40 inference(skolemize,[status(sab)],[195])).
% 4.89/3.40 tff(197,plain,
% 4.89/3.40 (![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[196, 189])).
% 4.89/3.40 tff(198,plain,
% 4.89/3.40 (p11(c15, c16) <=> p11(c15, c16)),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(199,axiom,(p11(c15, c16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_5')).
% 4.89/3.40 tff(200,plain,
% 4.89/3.40 (p11(c15, c16)),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[199, 198])).
% 4.89/3.40 tff(201,plain,
% 4.89/3.40 (((~![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))) | ((~p11(c15, c16)) | (~p9(c12, f6(c15))) | p8(c12, f6(c15), c15))) <=> ((~![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))) | (~p11(c15, c16)) | (~p9(c12, f6(c15))) | p8(c12, f6(c15), c15))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(202,plain,
% 4.89/3.40 (((~p9(c12, f6(c15))) | (~p11(c15, c16)) | p8(c12, f6(c15), c15)) <=> ((~p11(c15, c16)) | (~p9(c12, f6(c15))) | p8(c12, f6(c15), c15))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(203,plain,
% 4.89/3.40 (((~![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))) | ((~p9(c12, f6(c15))) | (~p11(c15, c16)) | p8(c12, f6(c15), c15))) <=> ((~![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))) | ((~p11(c15, c16)) | (~p9(c12, f6(c15))) | p8(c12, f6(c15), c15)))),
% 4.89/3.40 inference(monotonicity,[status(thm)],[202])).
% 4.89/3.40 tff(204,plain,
% 4.89/3.40 (((~![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))) | ((~p9(c12, f6(c15))) | (~p11(c15, c16)) | p8(c12, f6(c15), c15))) <=> ((~![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))) | (~p11(c15, c16)) | (~p9(c12, f6(c15))) | p8(c12, f6(c15), c15))),
% 4.89/3.40 inference(transitivity,[status(thm)],[203, 201])).
% 4.89/3.40 tff(205,plain,
% 4.89/3.40 ((~![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))) | ((~p9(c12, f6(c15))) | (~p11(c15, c16)) | p8(c12, f6(c15), c15))),
% 4.89/3.40 inference(quant_inst,[status(thm)],[])).
% 4.89/3.40 tff(206,plain,
% 4.89/3.40 ((~![X29: $i, X28: $i] : ((~p9(c12, X28)) | (~p11(X29, c16)) | p8(c12, X28, X29))) | (~p11(c15, c16)) | (~p9(c12, f6(c15))) | p8(c12, f6(c15), c15)),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[205, 204])).
% 4.89/3.40 tff(207,plain,
% 4.89/3.40 ($false),
% 4.89/3.40 inference(unit_resolution,[status(thm)],[206, 200, 197, 187, 186])).
% 4.89/3.40 tff(208,plain,(p8(c12, f6(c15), c15) | (~p9(c12, f6(c15)))), inference(lemma,lemma(discharge,[]))).
% 4.89/3.40 tff(209,plain,
% 4.89/3.40 (p8(c12, f6(c15), c15)),
% 4.89/3.40 inference(unit_resolution,[status(thm)],[208, 185])).
% 4.89/3.40 tff(210,plain,
% 4.89/3.40 (((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))) | ((~p9(c12, f6(c14))) | p8(c12, f6(c14), f3(c15)) | (~p8(c12, f6(c15), c15)))) <=> ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))) | (~p9(c12, f6(c14))) | p8(c12, f6(c14), f3(c15)) | (~p8(c12, f6(c15), c15)))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(211,plain,
% 4.89/3.40 ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))) | ((~p9(c12, f6(c14))) | p8(c12, f6(c14), f3(c15)) | (~p8(c12, f6(c15), c15)))),
% 4.89/3.40 inference(quant_inst,[status(thm)],[])).
% 4.89/3.40 tff(212,plain,
% 4.89/3.40 ((~![X31: $i, X30: $i] : ((~p9(c12, X30)) | p8(c12, X30, f3(X31)) | (~p8(c12, f6(X31), X31)))) | (~p9(c12, f6(c14))) | p8(c12, f6(c14), f3(c15)) | (~p8(c12, f6(c15), c15))),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[211, 210])).
% 4.89/3.40 tff(213,plain,
% 4.89/3.40 (p8(c12, f6(c14), f3(c15)) | (~p8(c12, f6(c15), c15))),
% 4.89/3.40 inference(unit_resolution,[status(thm)],[212, 118, 160])).
% 4.89/3.40 tff(214,plain,
% 4.89/3.40 (p8(c12, f6(c14), f3(c15))),
% 4.89/3.40 inference(unit_resolution,[status(thm)],[213, 209])).
% 4.89/3.40 tff(215,plain,
% 4.89/3.40 (((~![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))) | ((~p2(c14, f3(c15))) | p2(f3(c15), f3(c15)))) <=> ((~![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))) | (~p2(c14, f3(c15))) | p2(f3(c15), f3(c15)))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(216,plain,
% 4.89/3.40 (((~p2(c14, f3(c15))) | (~p2(c14, f3(c15))) | p2(f3(c15), f3(c15))) <=> ((~p2(c14, f3(c15))) | p2(f3(c15), f3(c15)))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(217,plain,
% 4.89/3.40 (((~![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))) | ((~p2(c14, f3(c15))) | (~p2(c14, f3(c15))) | p2(f3(c15), f3(c15)))) <=> ((~![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))) | ((~p2(c14, f3(c15))) | p2(f3(c15), f3(c15))))),
% 4.89/3.40 inference(monotonicity,[status(thm)],[216])).
% 4.89/3.40 tff(218,plain,
% 4.89/3.40 (((~![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))) | ((~p2(c14, f3(c15))) | (~p2(c14, f3(c15))) | p2(f3(c15), f3(c15)))) <=> ((~![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))) | (~p2(c14, f3(c15))) | p2(f3(c15), f3(c15)))),
% 4.89/3.40 inference(transitivity,[status(thm)],[217, 215])).
% 4.89/3.40 tff(219,plain,
% 4.89/3.40 ((~![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))) | ((~p2(c14, f3(c15))) | (~p2(c14, f3(c15))) | p2(f3(c15), f3(c15)))),
% 4.89/3.40 inference(quant_inst,[status(thm)],[])).
% 4.89/3.40 tff(220,plain,
% 4.89/3.40 ((~![X9: $i, X7: $i, X8: $i] : ((~p2(X7, X8)) | (~p2(X7, X9)) | p2(X8, X9))) | (~p2(c14, f3(c15))) | p2(f3(c15), f3(c15))),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[219, 218])).
% 4.89/3.40 tff(221,plain,
% 4.89/3.40 (p2(f3(c15), f3(c15))),
% 4.89/3.40 inference(unit_resolution,[status(thm)],[220, 27, 55])).
% 4.89/3.40 tff(222,plain,
% 4.89/3.40 (((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | ((~p2(f3(c15), f3(c15))) | (~p4(f6(c14), f6(f3(c15)))) | (~p7(c12, c12)) | (~p8(c12, f6(c14), f3(c15))) | p8(c12, f6(f3(c15)), f3(c15)))) <=> ((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | (~p2(f3(c15), f3(c15))) | (~p4(f6(c14), f6(f3(c15)))) | (~p7(c12, c12)) | (~p8(c12, f6(c14), f3(c15))) | p8(c12, f6(f3(c15)), f3(c15)))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(223,plain,
% 4.89/3.40 (((~p4(f6(c14), f6(f3(c15)))) | (~p8(c12, f6(c14), f3(c15))) | (~p7(c12, c12)) | (~p2(f3(c15), f3(c15))) | p8(c12, f6(f3(c15)), f3(c15))) <=> ((~p2(f3(c15), f3(c15))) | (~p4(f6(c14), f6(f3(c15)))) | (~p7(c12, c12)) | (~p8(c12, f6(c14), f3(c15))) | p8(c12, f6(f3(c15)), f3(c15)))),
% 4.89/3.40 inference(rewrite,[status(thm)],[])).
% 4.89/3.40 tff(224,plain,
% 4.89/3.40 (((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | ((~p4(f6(c14), f6(f3(c15)))) | (~p8(c12, f6(c14), f3(c15))) | (~p7(c12, c12)) | (~p2(f3(c15), f3(c15))) | p8(c12, f6(f3(c15)), f3(c15)))) <=> ((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | ((~p2(f3(c15), f3(c15))) | (~p4(f6(c14), f6(f3(c15)))) | (~p7(c12, c12)) | (~p8(c12, f6(c14), f3(c15))) | p8(c12, f6(f3(c15)), f3(c15))))),
% 4.89/3.40 inference(monotonicity,[status(thm)],[223])).
% 4.89/3.40 tff(225,plain,
% 4.89/3.40 (((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | ((~p4(f6(c14), f6(f3(c15)))) | (~p8(c12, f6(c14), f3(c15))) | (~p7(c12, c12)) | (~p2(f3(c15), f3(c15))) | p8(c12, f6(f3(c15)), f3(c15)))) <=> ((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | (~p2(f3(c15), f3(c15))) | (~p4(f6(c14), f6(f3(c15)))) | (~p7(c12, c12)) | (~p8(c12, f6(c14), f3(c15))) | p8(c12, f6(f3(c15)), f3(c15)))),
% 4.89/3.40 inference(transitivity,[status(thm)],[224, 222])).
% 4.89/3.40 tff(226,plain,
% 4.89/3.40 ((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | ((~p4(f6(c14), f6(f3(c15)))) | (~p8(c12, f6(c14), f3(c15))) | (~p7(c12, c12)) | (~p2(f3(c15), f3(c15))) | p8(c12, f6(f3(c15)), f3(c15)))),
% 4.89/3.40 inference(quant_inst,[status(thm)],[])).
% 4.89/3.40 tff(227,plain,
% 4.89/3.40 ((~![X25: $i, X27: $i, X22: $i, X23: $i, X26: $i, X24: $i] : ((~p4(X26, X23)) | (~p8(X27, X26, X25)) | (~p7(X27, X22)) | (~p2(X25, X24)) | p8(X22, X23, X24))) | (~p2(f3(c15), f3(c15))) | (~p4(f6(c14), f6(f3(c15)))) | (~p7(c12, c12)) | (~p8(c12, f6(c14), f3(c15))) | p8(c12, f6(f3(c15)), f3(c15))),
% 4.89/3.40 inference(modus_ponens,[status(thm)],[226, 225])).
% 4.89/3.40 tff(228,plain,
% 4.89/3.40 ($false),
% 4.89/3.40 inference(unit_resolution,[status(thm)],[227, 135, 221, 31, 68, 143, 214])).
% 4.89/3.40 % SZS output end Proof
%------------------------------------------------------------------------------