TSTP Solution File: SYN592-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN592-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 23:56:33 EDT 2022
% Result : Unsatisfiable 1.91s 1.48s
% Output : Proof 1.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN592-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Sep 5 06:04:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.91/1.48 % SZS status Unsatisfiable
% 1.91/1.48 % SZS output start Proof
% 1.91/1.48 tff(p3_type, type, (
% 1.91/1.48 p3: ( $i * $i ) > $o)).
% 1.91/1.48 tff(f4_type, type, (
% 1.91/1.48 f4: ( $i * $i ) > $i)).
% 1.91/1.48 tff(f5_type, type, (
% 1.91/1.48 f5: $i > $i)).
% 1.91/1.48 tff(c18_type, type, (
% 1.91/1.48 c18: $i)).
% 1.91/1.48 tff(c17_type, type, (
% 1.91/1.48 c17: $i)).
% 1.91/1.48 tff(f6_type, type, (
% 1.91/1.48 f6: $i > $i)).
% 1.91/1.48 tff(p2_type, type, (
% 1.91/1.48 p2: ( $i * $i ) > $o)).
% 1.91/1.48 tff(p12_type, type, (
% 1.91/1.48 p12: ( $i * $i ) > $o)).
% 1.91/1.48 tff(c14_type, type, (
% 1.91/1.48 c14: $i)).
% 1.91/1.48 tff(p7_type, type, (
% 1.91/1.48 p7: ( $i * $i ) > $o)).
% 1.91/1.48 tff(c13_type, type, (
% 1.91/1.48 c13: $i)).
% 1.91/1.48 tff(p11_type, type, (
% 1.91/1.48 p11: ( $i * $i ) > $o)).
% 1.91/1.48 tff(1,plain,
% 1.91/1.48 (^[X15: $i] : refl(p2(X15, X15) <=> p2(X15, X15))),
% 1.91/1.48 inference(bind,[status(th)],[])).
% 1.91/1.48 tff(2,plain,
% 1.91/1.48 (![X15: $i] : p2(X15, X15) <=> ![X15: $i] : p2(X15, X15)),
% 1.91/1.48 inference(quant_intro,[status(thm)],[1])).
% 1.91/1.48 tff(3,plain,
% 1.91/1.48 (![X15: $i] : p2(X15, X15) <=> ![X15: $i] : p2(X15, X15)),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(4,axiom,(![X15: $i] : p2(X15, X15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_4')).
% 1.91/1.48 tff(5,plain,
% 1.91/1.48 (![X15: $i] : p2(X15, X15)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.91/1.48 tff(6,plain,(
% 1.91/1.48 ![X15: $i] : p2(X15, X15)),
% 1.91/1.48 inference(skolemize,[status(sab)],[5])).
% 1.91/1.48 tff(7,plain,
% 1.91/1.48 (![X15: $i] : p2(X15, X15)),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.91/1.48 tff(8,plain,
% 1.91/1.48 ((~![X15: $i] : p2(X15, X15)) | p2(f6(c18), f6(c18))),
% 1.91/1.48 inference(quant_inst,[status(thm)],[])).
% 1.91/1.48 tff(9,plain,
% 1.91/1.48 (p2(f6(c18), f6(c18))),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.91/1.48 tff(10,plain,
% 1.91/1.48 (^[X20: $i] : refl(((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))) <=> ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))))),
% 1.91/1.48 inference(bind,[status(th)],[])).
% 1.91/1.48 tff(11,plain,
% 1.91/1.48 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))) <=> ![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 1.91/1.48 inference(quant_intro,[status(thm)],[10])).
% 1.91/1.48 tff(12,plain,
% 1.91/1.48 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))) <=> ![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(13,plain,
% 1.91/1.48 (^[X20: $i] : rewrite((p2(f6(X20), f5(X20)) | (~p12(c14, f4(X20, c17)))) <=> ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20))))),
% 1.91/1.48 inference(bind,[status(th)],[])).
% 1.91/1.48 tff(14,plain,
% 1.91/1.48 (![X20: $i] : (p2(f6(X20), f5(X20)) | (~p12(c14, f4(X20, c17)))) <=> ![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 1.91/1.48 inference(quant_intro,[status(thm)],[13])).
% 1.91/1.48 tff(15,axiom,(![X20: $i] : (p2(f6(X20), f5(X20)) | (~p12(c14, f4(X20, c17))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_22')).
% 1.91/1.48 tff(16,plain,
% 1.91/1.48 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[15, 14])).
% 1.91/1.48 tff(17,plain,
% 1.91/1.48 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[16, 12])).
% 1.91/1.48 tff(18,plain,(
% 1.91/1.48 ![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 1.91/1.48 inference(skolemize,[status(sab)],[17])).
% 1.91/1.48 tff(19,plain,
% 1.91/1.48 (![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[18, 11])).
% 1.91/1.48 tff(20,plain,
% 1.91/1.48 (p12(c14, f4(c18, c17)) <=> p12(c14, f4(c18, c17))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(21,axiom,(p12(c14, f4(c18, c17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_11')).
% 1.91/1.48 tff(22,plain,
% 1.91/1.48 (p12(c14, f4(c18, c17))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[21, 20])).
% 1.91/1.48 tff(23,plain,
% 1.91/1.48 (((~![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))) | ((~p12(c14, f4(c18, c17))) | p2(f6(c18), f5(c18)))) <=> ((~![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))) | (~p12(c14, f4(c18, c17))) | p2(f6(c18), f5(c18)))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(24,plain,
% 1.91/1.48 ((~![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))) | ((~p12(c14, f4(c18, c17))) | p2(f6(c18), f5(c18)))),
% 1.91/1.48 inference(quant_inst,[status(thm)],[])).
% 1.91/1.48 tff(25,plain,
% 1.91/1.48 ((~![X20: $i] : ((~p12(c14, f4(X20, c17))) | p2(f6(X20), f5(X20)))) | (~p12(c14, f4(c18, c17))) | p2(f6(c18), f5(c18))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.91/1.48 tff(26,plain,
% 1.91/1.48 (p2(f6(c18), f5(c18))),
% 1.91/1.48 inference(unit_resolution,[status(thm)],[25, 22, 19])).
% 1.91/1.48 tff(27,plain,
% 1.91/1.48 (^[X17: $i, X16: $i, X15: $i] : refl(((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17)) <=> ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17)))),
% 1.91/1.48 inference(bind,[status(th)],[])).
% 1.91/1.48 tff(28,plain,
% 1.91/1.48 (![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17)) <=> ![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 1.91/1.48 inference(quant_intro,[status(thm)],[27])).
% 1.91/1.48 tff(29,plain,
% 1.91/1.48 (![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17)) <=> ![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 1.91/1.48 inference(rewrite,[status(thm)],[])).
% 1.91/1.48 tff(30,plain,
% 1.91/1.48 (^[X17: $i, X16: $i, X15: $i] : trans(monotonicity(rewrite((p2(X16, X17) | (~p2(X15, X16))) <=> ((~p2(X15, X16)) | p2(X16, X17))), (((p2(X16, X17) | (~p2(X15, X16))) | (~p2(X15, X17))) <=> (((~p2(X15, X16)) | p2(X16, X17)) | (~p2(X15, X17))))), rewrite((((~p2(X15, X16)) | p2(X16, X17)) | (~p2(X15, X17))) <=> ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))), (((p2(X16, X17) | (~p2(X15, X16))) | (~p2(X15, X17))) <=> ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))))),
% 1.91/1.48 inference(bind,[status(th)],[])).
% 1.91/1.48 tff(31,plain,
% 1.91/1.48 (![X17: $i, X16: $i, X15: $i] : ((p2(X16, X17) | (~p2(X15, X16))) | (~p2(X15, X17))) <=> ![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 1.91/1.48 inference(quant_intro,[status(thm)],[30])).
% 1.91/1.48 tff(32,axiom,(![X17: $i, X16: $i, X15: $i] : ((p2(X16, X17) | (~p2(X15, X16))) | (~p2(X15, X17)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_20')).
% 1.91/1.48 tff(33,plain,
% 1.91/1.48 (![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 1.91/1.48 inference(modus_ponens,[status(thm)],[32, 31])).
% 1.91/1.48 tff(34,plain,
% 1.91/1.48 (![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[33, 29])).
% 1.91/1.49 tff(35,plain,(
% 1.91/1.49 ![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 1.91/1.49 inference(skolemize,[status(sab)],[34])).
% 1.91/1.49 tff(36,plain,
% 1.91/1.49 (![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[35, 28])).
% 1.91/1.49 tff(37,plain,
% 1.91/1.49 (((~![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))) | ((~p2(f6(c18), f5(c18))) | (~p2(f6(c18), f6(c18))) | p2(f5(c18), f6(c18)))) <=> ((~![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))) | (~p2(f6(c18), f5(c18))) | (~p2(f6(c18), f6(c18))) | p2(f5(c18), f6(c18)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(38,plain,
% 1.91/1.49 ((~![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))) | ((~p2(f6(c18), f5(c18))) | (~p2(f6(c18), f6(c18))) | p2(f5(c18), f6(c18)))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(39,plain,
% 1.91/1.49 ((~![X17: $i, X16: $i, X15: $i] : ((~p2(X15, X16)) | (~p2(X15, X17)) | p2(X16, X17))) | (~p2(f6(c18), f5(c18))) | (~p2(f6(c18), f6(c18))) | p2(f5(c18), f6(c18))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.91/1.49 tff(40,plain,
% 1.91/1.49 (p2(f5(c18), f6(c18))),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[39, 36, 26, 9])).
% 1.91/1.49 tff(41,plain,
% 1.91/1.49 ((~![X15: $i] : p2(X15, X15)) | p2(c17, c17)),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(42,plain,
% 1.91/1.49 (p2(c17, c17)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[41, 7])).
% 1.91/1.49 tff(43,plain,
% 1.91/1.49 (^[X27: $i, X29: $i, X28: $i, X26: $i] : refl(((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29))) <=> ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29))))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(44,plain,
% 1.91/1.49 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29))) <=> ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 1.91/1.49 inference(quant_intro,[status(thm)],[43])).
% 1.91/1.49 tff(45,plain,
% 1.91/1.49 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29))) <=> ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(46,plain,
% 1.91/1.49 (^[X27: $i, X29: $i, X28: $i, X26: $i] : trans(monotonicity(rewrite((p3(f4(X26, X27), f4(X28, X29)) | (~p2(X26, X28))) <=> ((~p2(X26, X28)) | p3(f4(X26, X27), f4(X28, X29)))), (((p3(f4(X26, X27), f4(X28, X29)) | (~p2(X26, X28))) | (~p2(X27, X29))) <=> (((~p2(X26, X28)) | p3(f4(X26, X27), f4(X28, X29))) | (~p2(X27, X29))))), rewrite((((~p2(X26, X28)) | p3(f4(X26, X27), f4(X28, X29))) | (~p2(X27, X29))) <=> ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))), (((p3(f4(X26, X27), f4(X28, X29)) | (~p2(X26, X28))) | (~p2(X27, X29))) <=> ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(47,plain,
% 1.91/1.49 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((p3(f4(X26, X27), f4(X28, X29)) | (~p2(X26, X28))) | (~p2(X27, X29))) <=> ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 1.91/1.49 inference(quant_intro,[status(thm)],[46])).
% 1.91/1.49 tff(48,axiom,(![X27: $i, X29: $i, X28: $i, X26: $i] : ((p3(f4(X26, X27), f4(X28, X29)) | (~p2(X26, X28))) | (~p2(X27, X29)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_26')).
% 1.91/1.49 tff(49,plain,
% 1.91/1.49 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.91/1.49 tff(50,plain,
% 1.91/1.49 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[49, 45])).
% 1.91/1.49 tff(51,plain,(
% 1.91/1.49 ![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 1.91/1.49 inference(skolemize,[status(sab)],[50])).
% 1.91/1.49 tff(52,plain,
% 1.91/1.49 (![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[51, 44])).
% 1.91/1.49 tff(53,plain,
% 1.91/1.49 (((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(c17, f5(c18)), f4(c17, f6(c18))))) <=> ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | (~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(c17, f5(c18)), f4(c17, f6(c18))))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(54,plain,
% 1.91/1.49 ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(c17, f5(c18)), f4(c17, f6(c18))))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(55,plain,
% 1.91/1.49 ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | (~p2(c17, c17)) | (~p2(f5(c18), f6(c18))) | p3(f4(c17, f5(c18)), f4(c17, f6(c18)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[54, 53])).
% 1.91/1.49 tff(56,plain,
% 1.91/1.49 (p3(f4(c17, f5(c18)), f4(c17, f6(c18)))),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[55, 52, 42, 40])).
% 1.91/1.49 tff(57,plain,
% 1.91/1.49 (^[X23: $i] : refl(p3(X23, X23) <=> p3(X23, X23))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(58,plain,
% 1.91/1.49 (![X23: $i] : p3(X23, X23) <=> ![X23: $i] : p3(X23, X23)),
% 1.91/1.49 inference(quant_intro,[status(thm)],[57])).
% 1.91/1.49 tff(59,plain,
% 1.91/1.49 (![X23: $i] : p3(X23, X23) <=> ![X23: $i] : p3(X23, X23)),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(60,axiom,(![X23: $i] : p3(X23, X23)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_5')).
% 1.91/1.49 tff(61,plain,
% 1.91/1.49 (![X23: $i] : p3(X23, X23)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.91/1.49 tff(62,plain,(
% 1.91/1.49 ![X23: $i] : p3(X23, X23)),
% 1.91/1.49 inference(skolemize,[status(sab)],[61])).
% 1.91/1.49 tff(63,plain,
% 1.91/1.49 (![X23: $i] : p3(X23, X23)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[62, 58])).
% 1.91/1.49 tff(64,plain,
% 1.91/1.49 ((~![X23: $i] : p3(X23, X23)) | p3(f4(c17, f5(c18)), f4(c17, f5(c18)))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(65,plain,
% 1.91/1.49 (p3(f4(c17, f5(c18)), f4(c17, f5(c18)))),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[64, 63])).
% 1.91/1.49 tff(66,plain,
% 1.91/1.49 (^[X25: $i, X23: $i, X24: $i] : refl(((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25)) <=> ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25)))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(67,plain,
% 1.91/1.49 (![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25)) <=> ![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))),
% 1.91/1.49 inference(quant_intro,[status(thm)],[66])).
% 1.91/1.49 tff(68,plain,
% 1.91/1.49 (![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25)) <=> ![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(69,plain,
% 1.91/1.49 (^[X25: $i, X23: $i, X24: $i] : trans(monotonicity(rewrite((p3(X24, X25) | (~p3(X23, X24))) <=> ((~p3(X23, X24)) | p3(X24, X25))), (((p3(X24, X25) | (~p3(X23, X24))) | (~p3(X23, X25))) <=> (((~p3(X23, X24)) | p3(X24, X25)) | (~p3(X23, X25))))), rewrite((((~p3(X23, X24)) | p3(X24, X25)) | (~p3(X23, X25))) <=> ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))), (((p3(X24, X25) | (~p3(X23, X24))) | (~p3(X23, X25))) <=> ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(70,plain,
% 1.91/1.49 (![X25: $i, X23: $i, X24: $i] : ((p3(X24, X25) | (~p3(X23, X24))) | (~p3(X23, X25))) <=> ![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))),
% 1.91/1.49 inference(quant_intro,[status(thm)],[69])).
% 1.91/1.49 tff(71,axiom,(![X25: $i, X23: $i, X24: $i] : ((p3(X24, X25) | (~p3(X23, X24))) | (~p3(X23, X25)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p3_21')).
% 1.91/1.49 tff(72,plain,
% 1.91/1.49 (![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.91/1.49 tff(73,plain,
% 1.91/1.49 (![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.91/1.49 tff(74,plain,(
% 1.91/1.49 ![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))),
% 1.91/1.49 inference(skolemize,[status(sab)],[73])).
% 1.91/1.49 tff(75,plain,
% 1.91/1.49 (![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.91/1.49 tff(76,plain,
% 1.91/1.49 (((~![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))) | ((~p3(f4(c17, f5(c18)), f4(c17, f5(c18)))) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | p3(f4(c17, f6(c18)), f4(c17, f5(c18))))) <=> ((~![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))) | (~p3(f4(c17, f5(c18)), f4(c17, f5(c18)))) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | p3(f4(c17, f6(c18)), f4(c17, f5(c18))))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(77,plain,
% 1.91/1.49 ((~![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))) | ((~p3(f4(c17, f5(c18)), f4(c17, f5(c18)))) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | p3(f4(c17, f6(c18)), f4(c17, f5(c18))))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(78,plain,
% 1.91/1.49 ((~![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))) | (~p3(f4(c17, f5(c18)), f4(c17, f5(c18)))) | (~p3(f4(c17, f5(c18)), f4(c17, f6(c18)))) | p3(f4(c17, f6(c18)), f4(c17, f5(c18)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.91/1.49 tff(79,plain,
% 1.91/1.49 (p3(f4(c17, f6(c18)), f4(c17, f5(c18)))),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[78, 75, 65, 56])).
% 1.91/1.49 tff(80,plain,
% 1.91/1.49 (^[X30: $i] : refl(p7(X30, X30) <=> p7(X30, X30))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(81,plain,
% 1.91/1.49 (![X30: $i] : p7(X30, X30) <=> ![X30: $i] : p7(X30, X30)),
% 1.91/1.49 inference(quant_intro,[status(thm)],[80])).
% 1.91/1.49 tff(82,plain,
% 1.91/1.49 (![X30: $i] : p7(X30, X30) <=> ![X30: $i] : p7(X30, X30)),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(83,axiom,(![X30: $i] : p7(X30, X30)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p7_3')).
% 1.91/1.49 tff(84,plain,
% 1.91/1.49 (![X30: $i] : p7(X30, X30)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.91/1.49 tff(85,plain,(
% 1.91/1.49 ![X30: $i] : p7(X30, X30)),
% 1.91/1.49 inference(skolemize,[status(sab)],[84])).
% 1.91/1.49 tff(86,plain,
% 1.91/1.49 (![X30: $i] : p7(X30, X30)),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[85, 81])).
% 1.91/1.49 tff(87,plain,
% 1.91/1.49 ((~![X30: $i] : p7(X30, X30)) | p7(c13, c13)),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(88,plain,
% 1.91/1.49 (p7(c13, c13)),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[87, 86])).
% 1.91/1.49 tff(89,plain,
% 1.91/1.49 (((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(f5(c18), f6(c18))) | (~p2(c17, c17)) | p3(f4(f5(c18), c17), f4(f6(c18), c17)))) <=> ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | (~p2(f5(c18), f6(c18))) | (~p2(c17, c17)) | p3(f4(f5(c18), c17), f4(f6(c18), c17)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(90,plain,
% 1.91/1.49 ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | ((~p2(f5(c18), f6(c18))) | (~p2(c17, c17)) | p3(f4(f5(c18), c17), f4(f6(c18), c17)))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(91,plain,
% 1.91/1.49 ((~![X27: $i, X29: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p2(X27, X29)) | p3(f4(X26, X27), f4(X28, X29)))) | (~p2(f5(c18), f6(c18))) | (~p2(c17, c17)) | p3(f4(f5(c18), c17), f4(f6(c18), c17))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.91/1.49 tff(92,plain,
% 1.91/1.49 (p3(f4(f5(c18), c17), f4(f6(c18), c17))),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[91, 52, 42, 40])).
% 1.91/1.49 tff(93,plain,
% 1.91/1.49 ((~![X23: $i] : p3(X23, X23)) | p3(f4(f5(c18), c17), f4(f5(c18), c17))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(94,plain,
% 1.91/1.49 (p3(f4(f5(c18), c17), f4(f5(c18), c17))),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[93, 63])).
% 1.91/1.49 tff(95,plain,
% 1.91/1.49 (((~![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))) | ((~p3(f4(f5(c18), c17), f4(f5(c18), c17))) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | p3(f4(f6(c18), c17), f4(f5(c18), c17)))) <=> ((~![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))) | (~p3(f4(f5(c18), c17), f4(f5(c18), c17))) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | p3(f4(f6(c18), c17), f4(f5(c18), c17)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(96,plain,
% 1.91/1.49 ((~![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))) | ((~p3(f4(f5(c18), c17), f4(f5(c18), c17))) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | p3(f4(f6(c18), c17), f4(f5(c18), c17)))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(97,plain,
% 1.91/1.49 ((~![X25: $i, X23: $i, X24: $i] : ((~p3(X23, X25)) | (~p3(X23, X24)) | p3(X24, X25))) | (~p3(f4(f5(c18), c17), f4(f5(c18), c17))) | (~p3(f4(f5(c18), c17), f4(f6(c18), c17))) | p3(f4(f6(c18), c17), f4(f5(c18), c17))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.91/1.49 tff(98,plain,
% 1.91/1.49 (p3(f4(f6(c18), c17), f4(f5(c18), c17))),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[97, 75, 94, 92])).
% 1.91/1.49 tff(99,assumption,(p11(c13, f4(f6(c18), c17))), introduced(assumption)).
% 1.91/1.49 tff(100,plain,
% 1.91/1.49 (^[X6: $i, X7: $i, X5: $i, X8: $i] : refl(((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)) <=> ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(101,plain,
% 1.91/1.49 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)) <=> ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 1.91/1.49 inference(quant_intro,[status(thm)],[100])).
% 1.91/1.49 tff(102,plain,
% 1.91/1.49 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)) <=> ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(103,plain,
% 1.91/1.49 (^[X6: $i, X7: $i, X5: $i, X8: $i] : trans(monotonicity(trans(monotonicity(rewrite((p11(X5, X6) | (~p3(X8, X6))) <=> ((~p3(X8, X6)) | p11(X5, X6))), (((p11(X5, X6) | (~p3(X8, X6))) | (~p7(X7, X5))) <=> (((~p3(X8, X6)) | p11(X5, X6)) | (~p7(X7, X5))))), rewrite((((~p3(X8, X6)) | p11(X5, X6)) | (~p7(X7, X5))) <=> ((~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))), (((p11(X5, X6) | (~p3(X8, X6))) | (~p7(X7, X5))) <=> ((~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)))), ((((p11(X5, X6) | (~p3(X8, X6))) | (~p7(X7, X5))) | (~p11(X7, X8))) <=> (((~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)) | (~p11(X7, X8))))), rewrite((((~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6)) | (~p11(X7, X8))) <=> ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))), ((((p11(X5, X6) | (~p3(X8, X6))) | (~p7(X7, X5))) | (~p11(X7, X8))) <=> ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(104,plain,
% 1.91/1.49 (![X6: $i, X7: $i, X5: $i, X8: $i] : (((p11(X5, X6) | (~p3(X8, X6))) | (~p7(X7, X5))) | (~p11(X7, X8))) <=> ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 1.91/1.49 inference(quant_intro,[status(thm)],[103])).
% 1.91/1.49 tff(105,axiom,(![X6: $i, X7: $i, X5: $i, X8: $i] : (((p11(X5, X6) | (~p3(X8, X6))) | (~p7(X7, X5))) | (~p11(X7, X8)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_25')).
% 1.91/1.49 tff(106,plain,
% 1.91/1.49 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.91/1.49 tff(107,plain,
% 1.91/1.49 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[106, 102])).
% 1.91/1.49 tff(108,plain,(
% 1.91/1.49 ![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 1.91/1.49 inference(skolemize,[status(sab)],[107])).
% 1.91/1.49 tff(109,plain,
% 1.91/1.49 (![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[108, 101])).
% 1.91/1.49 tff(110,plain,
% 1.91/1.49 ((~p11(c13, f4(f5(c18), c17))) <=> (~p11(c13, f4(f5(c18), c17)))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(111,axiom,(~p11(c13, f4(f5(c18), c17))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p11_13')).
% 1.91/1.49 tff(112,plain,
% 1.91/1.49 (~p11(c13, f4(f5(c18), c17))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[111, 110])).
% 1.91/1.49 tff(113,plain,
% 1.91/1.49 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | (p11(c13, f4(f5(c18), c17)) | (~p7(c13, c13)) | (~p11(c13, f4(f6(c18), c17))) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(f5(c18), c17)) | (~p7(c13, c13)) | (~p11(c13, f4(f6(c18), c17))) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(114,plain,
% 1.91/1.49 (((~p11(c13, f4(f6(c18), c17))) | (~p7(c13, c13)) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))) | p11(c13, f4(f5(c18), c17))) <=> (p11(c13, f4(f5(c18), c17)) | (~p7(c13, c13)) | (~p11(c13, f4(f6(c18), c17))) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(115,plain,
% 1.91/1.49 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | ((~p11(c13, f4(f6(c18), c17))) | (~p7(c13, c13)) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))) | p11(c13, f4(f5(c18), c17)))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | (p11(c13, f4(f5(c18), c17)) | (~p7(c13, c13)) | (~p11(c13, f4(f6(c18), c17))) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17)))))),
% 1.91/1.49 inference(monotonicity,[status(thm)],[114])).
% 1.91/1.49 tff(116,plain,
% 1.91/1.49 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | ((~p11(c13, f4(f6(c18), c17))) | (~p7(c13, c13)) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))) | p11(c13, f4(f5(c18), c17)))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(f5(c18), c17)) | (~p7(c13, c13)) | (~p11(c13, f4(f6(c18), c17))) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))))),
% 1.91/1.49 inference(transitivity,[status(thm)],[115, 113])).
% 1.91/1.49 tff(117,plain,
% 1.91/1.49 ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | ((~p11(c13, f4(f6(c18), c17))) | (~p7(c13, c13)) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17))) | p11(c13, f4(f5(c18), c17)))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(118,plain,
% 1.91/1.49 ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(f5(c18), c17)) | (~p7(c13, c13)) | (~p11(c13, f4(f6(c18), c17))) | (~p3(f4(f6(c18), c17), f4(f5(c18), c17)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.91/1.49 tff(119,plain,
% 1.91/1.49 ($false),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[118, 112, 109, 99, 88, 98])).
% 1.91/1.49 tff(120,plain,(~p11(c13, f4(f6(c18), c17))), inference(lemma,lemma(discharge,[]))).
% 1.91/1.49 tff(121,plain,
% 1.91/1.49 (^[X9: $i] : refl(((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9)))) <=> ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9)))))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(122,plain,
% 1.91/1.49 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9)))) <=> ![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 1.91/1.49 inference(quant_intro,[status(thm)],[121])).
% 1.91/1.49 tff(123,plain,
% 1.91/1.49 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9)))) <=> ![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(124,plain,
% 1.91/1.49 (^[X9: $i] : rewrite(((p11(c13, f4(c17, f6(X9))) | p11(c13, f4(f6(X9), c17))) | (~p12(c14, f4(X9, c17)))) <=> ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9)))))),
% 1.91/1.49 inference(bind,[status(th)],[])).
% 1.91/1.49 tff(125,plain,
% 1.91/1.49 (![X9: $i] : ((p11(c13, f4(c17, f6(X9))) | p11(c13, f4(f6(X9), c17))) | (~p12(c14, f4(X9, c17)))) <=> ![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 1.91/1.49 inference(quant_intro,[status(thm)],[124])).
% 1.91/1.49 tff(126,axiom,(![X9: $i] : ((p11(c13, f4(c17, f6(X9))) | p11(c13, f4(f6(X9), c17))) | (~p12(c14, f4(X9, c17))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_27')).
% 1.91/1.49 tff(127,plain,
% 1.91/1.49 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.91/1.49 tff(128,plain,
% 1.91/1.49 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[127, 123])).
% 1.91/1.49 tff(129,plain,(
% 1.91/1.49 ![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 1.91/1.49 inference(skolemize,[status(sab)],[128])).
% 1.91/1.49 tff(130,plain,
% 1.91/1.49 (![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[129, 122])).
% 1.91/1.49 tff(131,plain,
% 1.91/1.49 (((~![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))) | ((~p12(c14, f4(c18, c17))) | p11(c13, f4(f6(c18), c17)) | p11(c13, f4(c17, f6(c18))))) <=> ((~![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))) | (~p12(c14, f4(c18, c17))) | p11(c13, f4(f6(c18), c17)) | p11(c13, f4(c17, f6(c18))))),
% 1.91/1.49 inference(rewrite,[status(thm)],[])).
% 1.91/1.49 tff(132,plain,
% 1.91/1.49 ((~![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))) | ((~p12(c14, f4(c18, c17))) | p11(c13, f4(f6(c18), c17)) | p11(c13, f4(c17, f6(c18))))),
% 1.91/1.49 inference(quant_inst,[status(thm)],[])).
% 1.91/1.49 tff(133,plain,
% 1.91/1.49 ((~![X9: $i] : ((~p12(c14, f4(X9, c17))) | p11(c13, f4(f6(X9), c17)) | p11(c13, f4(c17, f6(X9))))) | (~p12(c14, f4(c18, c17))) | p11(c13, f4(f6(c18), c17)) | p11(c13, f4(c17, f6(c18)))),
% 1.91/1.49 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.91/1.49 tff(134,plain,
% 1.91/1.49 (p11(c13, f4(f6(c18), c17)) | p11(c13, f4(c17, f6(c18)))),
% 1.91/1.49 inference(unit_resolution,[status(thm)],[133, 22, 130])).
% 1.91/1.50 tff(135,plain,
% 1.91/1.50 (p11(c13, f4(c17, f6(c18)))),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[134, 120])).
% 1.91/1.50 tff(136,plain,
% 1.91/1.50 ((~p11(c13, f4(c17, f5(c18)))) <=> (~p11(c13, f4(c17, f5(c18))))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(137,axiom,(~p11(c13, f4(c17, f5(c18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p11_12')).
% 1.91/1.50 tff(138,plain,
% 1.91/1.50 (~p11(c13, f4(c17, f5(c18)))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[137, 136])).
% 1.91/1.50 tff(139,plain,
% 1.91/1.50 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | (p11(c13, f4(c17, f5(c18))) | (~p7(c13, c13)) | (~p11(c13, f4(c17, f6(c18)))) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(c17, f5(c18))) | (~p7(c13, c13)) | (~p11(c13, f4(c17, f6(c18)))) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(140,plain,
% 1.91/1.50 (((~p11(c13, f4(c17, f6(c18)))) | (~p7(c13, c13)) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | p11(c13, f4(c17, f5(c18)))) <=> (p11(c13, f4(c17, f5(c18))) | (~p7(c13, c13)) | (~p11(c13, f4(c17, f6(c18)))) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))))),
% 1.91/1.50 inference(rewrite,[status(thm)],[])).
% 1.91/1.50 tff(141,plain,
% 1.91/1.50 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | ((~p11(c13, f4(c17, f6(c18)))) | (~p7(c13, c13)) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | p11(c13, f4(c17, f5(c18))))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | (p11(c13, f4(c17, f5(c18))) | (~p7(c13, c13)) | (~p11(c13, f4(c17, f6(c18)))) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18))))))),
% 1.91/1.50 inference(monotonicity,[status(thm)],[140])).
% 1.91/1.50 tff(142,plain,
% 1.91/1.50 (((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | ((~p11(c13, f4(c17, f6(c18)))) | (~p7(c13, c13)) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | p11(c13, f4(c17, f5(c18))))) <=> ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(c17, f5(c18))) | (~p7(c13, c13)) | (~p11(c13, f4(c17, f6(c18)))) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))))),
% 1.91/1.50 inference(transitivity,[status(thm)],[141, 139])).
% 1.91/1.50 tff(143,plain,
% 1.91/1.50 ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | ((~p11(c13, f4(c17, f6(c18)))) | (~p7(c13, c13)) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18)))) | p11(c13, f4(c17, f5(c18))))),
% 1.91/1.50 inference(quant_inst,[status(thm)],[])).
% 1.91/1.50 tff(144,plain,
% 1.91/1.50 ((~![X6: $i, X7: $i, X5: $i, X8: $i] : ((~p11(X7, X8)) | (~p7(X7, X5)) | (~p3(X8, X6)) | p11(X5, X6))) | p11(c13, f4(c17, f5(c18))) | (~p7(c13, c13)) | (~p11(c13, f4(c17, f6(c18)))) | (~p3(f4(c17, f6(c18)), f4(c17, f5(c18))))),
% 1.91/1.50 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.91/1.50 tff(145,plain,
% 1.91/1.50 ($false),
% 1.91/1.50 inference(unit_resolution,[status(thm)],[144, 138, 109, 135, 88, 79])).
% 1.91/1.50 % SZS output end Proof
%------------------------------------------------------------------------------