TSTP Solution File: SYN581-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN581-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 1.72s 1.34s
% Output : Proof 1.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYN581-1 : TPTP v8.1.0. Released v2.5.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Sep 5 05:52:44 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 1.72/1.34 % SZS status Unsatisfiable
% 1.72/1.34 % SZS output start Proof
% 1.72/1.34 tff(p2_type, type, (
% 1.72/1.34 p2: ( $i * $i ) > $o)).
% 1.72/1.34 tff(f4_type, type, (
% 1.72/1.34 f4: $i > $i)).
% 1.72/1.34 tff(f6_type, type, (
% 1.72/1.34 f6: ( $i * $i ) > $i)).
% 1.72/1.34 tff(c18_type, type, (
% 1.72/1.34 c18: $i)).
% 1.72/1.34 tff(c15_type, type, (
% 1.72/1.34 c15: $i)).
% 1.72/1.34 tff(c14_type, type, (
% 1.72/1.34 c14: $i)).
% 1.72/1.34 tff(p5_type, type, (
% 1.72/1.34 p5: ( $i * $i ) > $o)).
% 1.72/1.34 tff(c16_type, type, (
% 1.72/1.34 c16: $i)).
% 1.72/1.34 tff(p11_type, type, (
% 1.72/1.34 p11: ( $i * $i ) > $o)).
% 1.72/1.34 tff(1,assumption,(~p2(f6(c15, c14), f6(c15, c18))), introduced(assumption)).
% 1.72/1.34 tff(2,plain,
% 1.72/1.34 (^[X31: $i] : refl(p5(X31, X31) <=> p5(X31, X31))),
% 1.72/1.34 inference(bind,[status(th)],[])).
% 1.72/1.34 tff(3,plain,
% 1.72/1.34 (![X31: $i] : p5(X31, X31) <=> ![X31: $i] : p5(X31, X31)),
% 1.72/1.34 inference(quant_intro,[status(thm)],[2])).
% 1.72/1.34 tff(4,plain,
% 1.72/1.34 (![X31: $i] : p5(X31, X31) <=> ![X31: $i] : p5(X31, X31)),
% 1.72/1.34 inference(rewrite,[status(thm)],[])).
% 1.72/1.34 tff(5,axiom,(![X31: $i] : p5(X31, X31)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p5_3')).
% 1.72/1.34 tff(6,plain,
% 1.72/1.34 (![X31: $i] : p5(X31, X31)),
% 1.72/1.34 inference(modus_ponens,[status(thm)],[5, 4])).
% 1.72/1.34 tff(7,plain,(
% 1.72/1.34 ![X31: $i] : p5(X31, X31)),
% 1.72/1.34 inference(skolemize,[status(sab)],[6])).
% 1.72/1.34 tff(8,plain,
% 1.72/1.34 (![X31: $i] : p5(X31, X31)),
% 1.72/1.34 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.72/1.34 tff(9,plain,
% 1.72/1.34 ((~![X31: $i] : p5(X31, X31)) | p5(c15, c15)),
% 1.72/1.34 inference(quant_inst,[status(thm)],[])).
% 1.72/1.34 tff(10,plain,
% 1.72/1.34 (p5(c15, c15)),
% 1.72/1.34 inference(unit_resolution,[status(thm)],[9, 8])).
% 1.72/1.34 tff(11,plain,
% 1.72/1.34 (^[X25: $i, X27: $i, X28: $i, X26: $i] : refl(((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28))) <=> ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28))))),
% 1.72/1.34 inference(bind,[status(th)],[])).
% 1.72/1.34 tff(12,plain,
% 1.72/1.34 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28))) <=> ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 1.72/1.34 inference(quant_intro,[status(thm)],[11])).
% 1.72/1.34 tff(13,plain,
% 1.72/1.34 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28))) <=> ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(14,plain,
% 1.72/1.35 (^[X25: $i, X27: $i, X28: $i, X26: $i] : trans(monotonicity(rewrite((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) <=> ((~p2(X26, X28)) | p2(f6(X25, X26), f6(X27, X28)))), (((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) | (~p5(X25, X27))) <=> (((~p2(X26, X28)) | p2(f6(X25, X26), f6(X27, X28))) | (~p5(X25, X27))))), rewrite((((~p2(X26, X28)) | p2(f6(X25, X26), f6(X27, X28))) | (~p5(X25, X27))) <=> ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))), (((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) | (~p5(X25, X27))) <=> ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))))),
% 1.72/1.35 inference(bind,[status(th)],[])).
% 1.72/1.35 tff(15,plain,
% 1.72/1.35 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) | (~p5(X25, X27))) <=> ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 1.72/1.35 inference(quant_intro,[status(thm)],[14])).
% 1.72/1.35 tff(16,axiom,(![X25: $i, X27: $i, X28: $i, X26: $i] : ((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) | (~p5(X25, X27)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_23')).
% 1.72/1.35 tff(17,plain,
% 1.72/1.35 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.72/1.35 tff(18,plain,
% 1.72/1.35 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.72/1.35 tff(19,plain,(
% 1.72/1.35 ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 1.72/1.35 inference(skolemize,[status(sab)],[18])).
% 1.72/1.35 tff(20,plain,
% 1.72/1.35 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.72/1.35 tff(21,plain,
% 1.72/1.35 (p2(c18, c14) <=> p2(c18, c14)),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(22,axiom,(p2(c18, c14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_5')).
% 1.72/1.35 tff(23,plain,
% 1.72/1.35 (p2(c18, c14)),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[22, 21])).
% 1.72/1.35 tff(24,plain,
% 1.72/1.35 (((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | ((~p2(c18, c14)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c14)))) <=> ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | (~p2(c18, c14)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c14)))),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(25,plain,
% 1.72/1.35 ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | ((~p2(c18, c14)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c14)))),
% 1.72/1.35 inference(quant_inst,[status(thm)],[])).
% 1.72/1.35 tff(26,plain,
% 1.72/1.35 ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | (~p2(c18, c14)) | (~p5(c15, c15)) | p2(f6(c15, c18), f6(c15, c14))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[25, 24])).
% 1.72/1.35 tff(27,plain,
% 1.72/1.35 (p2(f6(c15, c18), f6(c15, c14))),
% 1.72/1.35 inference(unit_resolution,[status(thm)],[26, 23, 20, 10])).
% 1.72/1.35 tff(28,plain,
% 1.72/1.35 (^[X18: $i] : refl(p2(X18, X18) <=> p2(X18, X18))),
% 1.72/1.35 inference(bind,[status(th)],[])).
% 1.72/1.35 tff(29,plain,
% 1.72/1.35 (![X18: $i] : p2(X18, X18) <=> ![X18: $i] : p2(X18, X18)),
% 1.72/1.35 inference(quant_intro,[status(thm)],[28])).
% 1.72/1.35 tff(30,plain,
% 1.72/1.35 (![X18: $i] : p2(X18, X18) <=> ![X18: $i] : p2(X18, X18)),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(31,axiom,(![X18: $i] : p2(X18, X18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_2')).
% 1.72/1.35 tff(32,plain,
% 1.72/1.35 (![X18: $i] : p2(X18, X18)),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[31, 30])).
% 1.72/1.35 tff(33,plain,(
% 1.72/1.35 ![X18: $i] : p2(X18, X18)),
% 1.72/1.35 inference(skolemize,[status(sab)],[32])).
% 1.72/1.35 tff(34,plain,
% 1.72/1.35 (![X18: $i] : p2(X18, X18)),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[33, 29])).
% 1.72/1.35 tff(35,plain,
% 1.72/1.35 ((~![X18: $i] : p2(X18, X18)) | p2(f6(c15, c18), f6(c15, c18))),
% 1.72/1.35 inference(quant_inst,[status(thm)],[])).
% 1.72/1.35 tff(36,plain,
% 1.72/1.35 (p2(f6(c15, c18), f6(c15, c18))),
% 1.72/1.35 inference(unit_resolution,[status(thm)],[35, 34])).
% 1.72/1.35 tff(37,plain,
% 1.72/1.35 (^[X18: $i, X20: $i, X19: $i] : refl((p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))))),
% 1.72/1.35 inference(bind,[status(th)],[])).
% 1.72/1.35 tff(38,plain,
% 1.72/1.35 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 1.72/1.35 inference(quant_intro,[status(thm)],[37])).
% 1.72/1.35 tff(39,plain,
% 1.72/1.35 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(40,plain,
% 1.72/1.35 (^[X18: $i, X20: $i, X19: $i] : trans(monotonicity(rewrite((p2(X19, X20) | (~p2(X18, X19))) <=> (p2(X19, X20) | (~p2(X18, X19)))), (((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))))), rewrite(((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))), (((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))))),
% 1.72/1.35 inference(bind,[status(th)],[])).
% 1.72/1.35 tff(41,plain,
% 1.72/1.35 (![X18: $i, X20: $i, X19: $i] : ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 1.72/1.35 inference(quant_intro,[status(thm)],[40])).
% 1.72/1.35 tff(42,axiom,(![X18: $i, X20: $i, X19: $i] : ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_18')).
% 1.72/1.35 tff(43,plain,
% 1.72/1.35 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.72/1.35 tff(44,plain,
% 1.72/1.35 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[43, 39])).
% 1.72/1.35 tff(45,plain,(
% 1.72/1.35 ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 1.72/1.35 inference(skolemize,[status(sab)],[44])).
% 1.72/1.35 tff(46,plain,
% 1.72/1.35 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[45, 38])).
% 1.72/1.35 tff(47,plain,
% 1.72/1.35 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | ((~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14))) | p2(f6(c15, c14), f6(c15, c18)))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14))) | p2(f6(c15, c14), f6(c15, c18)))),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(48,plain,
% 1.72/1.35 ((p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14)))) <=> ((~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14))) | p2(f6(c15, c14), f6(c15, c18)))),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(49,plain,
% 1.72/1.35 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | ((~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14))) | p2(f6(c15, c14), f6(c15, c18))))),
% 1.72/1.35 inference(monotonicity,[status(thm)],[48])).
% 1.72/1.35 tff(50,plain,
% 1.72/1.35 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14))) | p2(f6(c15, c14), f6(c15, c18)))),
% 1.72/1.35 inference(transitivity,[status(thm)],[49, 47])).
% 1.72/1.35 tff(51,plain,
% 1.72/1.35 ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f6(c15, c14), f6(c15, c18)) | (~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14))))),
% 1.72/1.35 inference(quant_inst,[status(thm)],[])).
% 1.72/1.35 tff(52,plain,
% 1.72/1.35 ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (~p2(f6(c15, c18), f6(c15, c18))) | (~p2(f6(c15, c18), f6(c15, c14))) | p2(f6(c15, c14), f6(c15, c18))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.72/1.35 tff(53,plain,
% 1.72/1.35 ($false),
% 1.72/1.35 inference(unit_resolution,[status(thm)],[52, 46, 36, 27, 1])).
% 1.72/1.35 tff(54,plain,(p2(f6(c15, c14), f6(c15, c18))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.35 tff(55,plain,
% 1.72/1.35 (^[X23: $i, X24: $i] : refl(((~p2(X23, X24)) | p2(f4(X23), f4(X24))) <=> ((~p2(X23, X24)) | p2(f4(X23), f4(X24))))),
% 1.72/1.35 inference(bind,[status(th)],[])).
% 1.72/1.35 tff(56,plain,
% 1.72/1.35 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24))) <=> ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 1.72/1.35 inference(quant_intro,[status(thm)],[55])).
% 1.72/1.35 tff(57,plain,
% 1.72/1.35 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24))) <=> ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(58,plain,
% 1.72/1.35 (^[X23: $i, X24: $i] : rewrite((p2(f4(X23), f4(X24)) | (~p2(X23, X24))) <=> ((~p2(X23, X24)) | p2(f4(X23), f4(X24))))),
% 1.72/1.35 inference(bind,[status(th)],[])).
% 1.72/1.35 tff(59,plain,
% 1.72/1.35 (![X23: $i, X24: $i] : (p2(f4(X23), f4(X24)) | (~p2(X23, X24))) <=> ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 1.72/1.35 inference(quant_intro,[status(thm)],[58])).
% 1.72/1.35 tff(60,axiom,(![X23: $i, X24: $i] : (p2(f4(X23), f4(X24)) | (~p2(X23, X24)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p2_14')).
% 1.72/1.35 tff(61,plain,
% 1.72/1.35 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.72/1.35 tff(62,plain,
% 1.72/1.35 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[61, 57])).
% 1.72/1.35 tff(63,plain,(
% 1.72/1.35 ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 1.72/1.35 inference(skolemize,[status(sab)],[62])).
% 1.72/1.35 tff(64,plain,
% 1.72/1.35 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[63, 56])).
% 1.72/1.35 tff(65,plain,
% 1.72/1.35 (((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | ((~p2(f6(c15, c14), f6(c15, c18))) | p2(f4(f6(c15, c14)), f4(f6(c15, c18))))) <=> ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | (~p2(f6(c15, c14), f6(c15, c18))) | p2(f4(f6(c15, c14)), f4(f6(c15, c18))))),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(66,plain,
% 1.72/1.35 ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | ((~p2(f6(c15, c14), f6(c15, c18))) | p2(f4(f6(c15, c14)), f4(f6(c15, c18))))),
% 1.72/1.35 inference(quant_inst,[status(thm)],[])).
% 1.72/1.35 tff(67,plain,
% 1.72/1.35 ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | (~p2(f6(c15, c14), f6(c15, c18))) | p2(f4(f6(c15, c14)), f4(f6(c15, c18)))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.72/1.35 tff(68,plain,
% 1.72/1.35 ((~p2(f6(c15, c14), f6(c15, c18))) | p2(f4(f6(c15, c14)), f4(f6(c15, c18)))),
% 1.72/1.35 inference(unit_resolution,[status(thm)],[67, 64])).
% 1.72/1.35 tff(69,plain,
% 1.72/1.35 (p2(f4(f6(c15, c14)), f4(f6(c15, c18)))),
% 1.72/1.35 inference(unit_resolution,[status(thm)],[68, 54])).
% 1.72/1.35 tff(70,plain,
% 1.72/1.35 ((~![X18: $i] : p2(X18, X18)) | p2(c16, c16)),
% 1.72/1.35 inference(quant_inst,[status(thm)],[])).
% 1.72/1.35 tff(71,plain,
% 1.72/1.35 (p2(c16, c16)),
% 1.72/1.35 inference(unit_resolution,[status(thm)],[70, 34])).
% 1.72/1.35 tff(72,plain,
% 1.72/1.35 (^[X9: $i, X10: $i, X7: $i, X8: $i] : refl(((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8)) <=> ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8)))),
% 1.72/1.35 inference(bind,[status(th)],[])).
% 1.72/1.35 tff(73,plain,
% 1.72/1.35 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8)) <=> ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 1.72/1.35 inference(quant_intro,[status(thm)],[72])).
% 1.72/1.35 tff(74,plain,
% 1.72/1.35 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8)) <=> ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(75,plain,
% 1.72/1.35 (^[X9: $i, X10: $i, X7: $i, X8: $i] : trans(monotonicity(trans(monotonicity(rewrite((p11(X7, X8) | (~p2(X9, X7))) <=> ((~p2(X9, X7)) | p11(X7, X8))), (((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) <=> (((~p2(X9, X7)) | p11(X7, X8)) | (~p2(X10, X8))))), rewrite((((~p2(X9, X7)) | p11(X7, X8)) | (~p2(X10, X8))) <=> ((~p2(X10, X8)) | (~p2(X9, X7)) | p11(X7, X8))), (((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) <=> ((~p2(X10, X8)) | (~p2(X9, X7)) | p11(X7, X8)))), ((((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) | (~p11(X9, X10))) <=> (((~p2(X10, X8)) | (~p2(X9, X7)) | p11(X7, X8)) | (~p11(X9, X10))))), rewrite((((~p2(X10, X8)) | (~p2(X9, X7)) | p11(X7, X8)) | (~p11(X9, X10))) <=> ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))), ((((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) | (~p11(X9, X10))) <=> ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))))),
% 1.72/1.35 inference(bind,[status(th)],[])).
% 1.72/1.35 tff(76,plain,
% 1.72/1.35 (![X9: $i, X10: $i, X7: $i, X8: $i] : (((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) | (~p11(X9, X10))) <=> ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 1.72/1.35 inference(quant_intro,[status(thm)],[75])).
% 1.72/1.35 tff(77,axiom,(![X9: $i, X10: $i, X7: $i, X8: $i] : (((p11(X7, X8) | (~p2(X9, X7))) | (~p2(X10, X8))) | (~p11(X9, X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_21')).
% 1.72/1.35 tff(78,plain,
% 1.72/1.35 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[77, 76])).
% 1.72/1.35 tff(79,plain,
% 1.72/1.35 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[78, 74])).
% 1.72/1.35 tff(80,plain,(
% 1.72/1.35 ![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 1.72/1.35 inference(skolemize,[status(sab)],[79])).
% 1.72/1.35 tff(81,plain,
% 1.72/1.35 (![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[80, 73])).
% 1.72/1.35 tff(82,plain,
% 1.72/1.35 ((~p11(f4(f6(c15, c18)), c16)) <=> (~p11(f4(f6(c15, c18)), c16))),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(83,axiom,(~p11(f4(f6(c15, c18)), c16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','not_p11_9')).
% 1.72/1.35 tff(84,plain,
% 1.72/1.35 (~p11(f4(f6(c15, c18)), c16)),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.72/1.35 tff(85,plain,
% 1.72/1.35 (p11(f4(f6(c15, c14)), c16) <=> p11(f4(f6(c15, c14)), c16)),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(86,axiom,(p11(f4(f6(c15, c14)), c16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','p11_8')).
% 1.72/1.35 tff(87,plain,
% 1.72/1.35 (p11(f4(f6(c15, c14)), c16)),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.72/1.35 tff(88,plain,
% 1.72/1.35 (((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | ((~p2(c16, c16)) | (~p11(f4(f6(c15, c14)), c16)) | (~p2(f4(f6(c15, c14)), f4(f6(c15, c18)))) | p11(f4(f6(c15, c18)), c16))) <=> ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | (~p2(c16, c16)) | (~p11(f4(f6(c15, c14)), c16)) | (~p2(f4(f6(c15, c14)), f4(f6(c15, c18)))) | p11(f4(f6(c15, c18)), c16))),
% 1.72/1.35 inference(rewrite,[status(thm)],[])).
% 1.72/1.35 tff(89,plain,
% 1.72/1.35 ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | ((~p2(c16, c16)) | (~p11(f4(f6(c15, c14)), c16)) | (~p2(f4(f6(c15, c14)), f4(f6(c15, c18)))) | p11(f4(f6(c15, c18)), c16))),
% 1.72/1.35 inference(quant_inst,[status(thm)],[])).
% 1.72/1.35 tff(90,plain,
% 1.72/1.35 ((~![X9: $i, X10: $i, X7: $i, X8: $i] : ((~p2(X10, X8)) | (~p11(X9, X10)) | (~p2(X9, X7)) | p11(X7, X8))) | (~p2(c16, c16)) | (~p11(f4(f6(c15, c14)), c16)) | (~p2(f4(f6(c15, c14)), f4(f6(c15, c18)))) | p11(f4(f6(c15, c18)), c16)),
% 1.72/1.35 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.72/1.35 tff(91,plain,
% 1.72/1.35 ($false),
% 1.72/1.35 inference(unit_resolution,[status(thm)],[90, 87, 84, 81, 71, 69])).
% 1.72/1.35 % SZS output end Proof
%------------------------------------------------------------------------------