TSTP Solution File: KRS105+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS105+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:44:46 EDT 2022
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KRS105+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n011.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 : Thu Sep 1 09:31:12 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.
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 tff(rr_type, type, (
% 0.14/0.40 rr: ( $i * $i ) > $o)).
% 0.14/0.40 tff(tptp_fun_Y_2_type, type, (
% 0.14/0.40 tptp_fun_Y_2: $i > $i)).
% 0.14/0.40 tff(i2003_11_14_17_20_53634_type, type, (
% 0.14/0.40 i2003_11_14_17_20_53634: $i)).
% 0.14/0.40 tff(cc_type, type, (
% 0.14/0.40 cc: $i > $o)).
% 0.14/0.40 tff(ca_Ax2_type, type, (
% 0.14/0.40 ca_Ax2: $i > $o)).
% 0.14/0.40 tff(cd_type, type, (
% 0.14/0.40 cd: $i > $o)).
% 0.14/0.40 tff(ra_Px1_type, type, (
% 0.14/0.40 ra_Px1: ( $i * $i ) > $o)).
% 0.14/0.40 tff(tptp_fun_Y_0_type, type, (
% 0.14/0.40 tptp_fun_Y_0: $i > $i)).
% 0.14/0.40 tff(tptp_fun_Y0_1_type, type, (
% 0.14/0.40 tptp_fun_Y0_1: $i > $i)).
% 0.14/0.40 tff(cdxcomp_type, type, (
% 0.14/0.40 cdxcomp: $i > $o)).
% 0.14/0.40 tff(cUnsatisfiable_type, type, (
% 0.14/0.40 cUnsatisfiable: $i > $o)).
% 0.14/0.40 tff(1,assumption,((~(cd(i2003_11_14_17_20_53634) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y_0(i2003_11_14_17_20_53634)))) | (~((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))))), introduced(assumption)).
% 0.14/0.40 tff(2,plain,
% 0.14/0.40 (^[X: $i] : rewrite((~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))))) <=> (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(3,plain,
% 0.14/0.40 (![X: $i] : (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))))) <=> ![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.14/0.40 tff(4,plain,
% 0.14/0.40 (^[X: $i] : refl((~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))))) <=> (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(5,plain,
% 0.14/0.40 (![X: $i] : (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))))) <=> ![X: $i] : (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[4])).
% 0.14/0.40 tff(6,plain,
% 0.14/0.40 (^[X: $i] : rewrite((~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))))) <=> (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(7,plain,
% 0.14/0.40 (![X: $i] : (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))))) <=> ![X: $i] : (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.40 tff(8,plain,
% 0.14/0.40 (![X: $i] : (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))))) <=> ![X: $i] : (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[7, 5])).
% 0.14/0.40 tff(9,plain,
% 0.14/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))) <=> ((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))), ((((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))) & (cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) <=> (((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))) & (cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))))), rewrite((((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))) & (cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) <=> (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X))))))), ((((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))) & (cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) <=> (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(10,plain,
% 0.14/0.40 (![X: $i] : (((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))) & (cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) <=> ![X: $i] : (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.14/0.40 tff(11,plain,
% 0.14/0.40 (![X: $i] : (cd(X) <=> (~?[Y: $i] : ra_Px1(X, Y))) <=> ![X: $i] : (cd(X) <=> (~?[Y: $i] : ra_Px1(X, Y)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(12,axiom,(![X: $i] : (cd(X) <=> (~?[Y: $i] : ra_Px1(X, Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_5')).
% 0.14/0.40 tff(13,plain,
% 0.14/0.40 (![X: $i] : (cd(X) <=> (~?[Y: $i] : ra_Px1(X, Y)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.14/0.40 tff(14,plain,(
% 0.14/0.40 ![X: $i] : (((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))) & (cd(X) | ra_Px1(X, tptp_fun_Y_0(X))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[13])).
% 0.14/0.40 tff(15,plain,
% 0.14/0.40 (![X: $i] : (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.14/0.40 tff(16,plain,
% 0.14/0.40 (![X: $i] : (~((~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y)))) | (~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[15, 8])).
% 0.14/0.40 tff(17,plain,
% 0.14/0.40 (![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[16, 3])).
% 0.14/0.40 tff(18,plain,
% 0.14/0.40 ((~![X: $i] : (~((~(cd(X) | ra_Px1(X, tptp_fun_Y_0(X)))) | (~((~cd(X)) | ![Y: $i] : (~ra_Px1(X, Y))))))) | (~((~(cd(i2003_11_14_17_20_53634) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y_0(i2003_11_14_17_20_53634)))) | (~((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(19,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[18, 17, 1])).
% 0.14/0.40 tff(20,plain,(~((~(cd(i2003_11_14_17_20_53634) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y_0(i2003_11_14_17_20_53634)))) | (~((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(21,plain,
% 0.14/0.40 (((~(cd(i2003_11_14_17_20_53634) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y_0(i2003_11_14_17_20_53634)))) | (~((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))))) | ((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(22,plain,
% 0.14/0.40 ((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.14/0.40 tff(23,assumption,(![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))), introduced(assumption)).
% 0.14/0.40 tff(24,plain,
% 0.14/0.40 (^[X: $i] : refl((~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(25,plain,
% 0.14/0.40 (![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.14/0.40 tff(26,plain,
% 0.14/0.40 (^[X: $i] : rewrite((~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(27,plain,
% 0.14/0.40 (![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.14/0.40 tff(28,plain,
% 0.14/0.40 (![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))) <=> ![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[27, 25])).
% 0.14/0.40 tff(29,plain,
% 0.14/0.40 (^[X: $i] : trans(monotonicity(rewrite((cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))) <=> (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))), ((((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X))) & (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X))) & (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))))), rewrite((((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X))) & (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))), ((((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X))) & (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(30,plain,
% 0.14/0.40 (![X: $i] : (((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X))) & (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0)))) <=> ![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[29])).
% 0.14/0.40 tff(31,plain,
% 0.14/0.40 (![X: $i] : (cdxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0)) <=> ![X: $i] : (cdxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(32,axiom,(![X: $i] : (cdxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_6')).
% 0.14/0.40 tff(33,plain,
% 0.14/0.40 (![X: $i] : (cdxcomp(X) <=> ?[Y0: $i] : ra_Px1(X, Y0))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.14/0.40 tff(34,plain,(
% 0.14/0.40 ![X: $i] : (((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X))) & (cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))),
% 0.14/0.40 inference(skolemize,[status(sab)],[33])).
% 0.14/0.40 tff(35,plain,
% 0.14/0.40 (![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.14/0.40 tff(36,plain,
% 0.14/0.40 (![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.14/0.40 tff(37,plain,
% 0.14/0.40 ((~![X: $i] : (~((~((~cdxcomp(X)) | ra_Px1(X, tptp_fun_Y0_1(X)))) | (~(cdxcomp(X) | ![Y0: $i] : (~ra_Px1(X, Y0))))))) | (~((~((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))) | (~(cdxcomp(i2003_11_14_17_20_53634) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y0))))))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(38,plain,
% 0.14/0.40 (~((~((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))) | (~(cdxcomp(i2003_11_14_17_20_53634) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y0)))))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.14/0.40 tff(39,plain,
% 0.14/0.40 (((~((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))) | (~(cdxcomp(i2003_11_14_17_20_53634) | ![Y0: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y0))))) | ((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(40,plain,
% 0.14/0.40 ((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.14/0.40 tff(41,plain,
% 0.14/0.40 (cUnsatisfiable(i2003_11_14_17_20_53634) <=> cUnsatisfiable(i2003_11_14_17_20_53634)),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(42,axiom,(cUnsatisfiable(i2003_11_14_17_20_53634)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_9')).
% 0.14/0.40 tff(43,plain,
% 0.14/0.40 (cUnsatisfiable(i2003_11_14_17_20_53634)),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.14/0.40 tff(44,plain,
% 0.14/0.40 (^[X: $i] : refl((cdxcomp(X) | (~cUnsatisfiable(X))) <=> (cdxcomp(X) | (~cUnsatisfiable(X))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(45,plain,
% 0.14/0.40 (![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X))) <=> ![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.14/0.40 tff(46,plain,
% 0.14/0.40 (![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X))) <=> ![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(47,plain,
% 0.14/0.40 (^[X: $i] : rewrite((cUnsatisfiable(X) => cdxcomp(X)) <=> (cdxcomp(X) | (~cUnsatisfiable(X))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(48,plain,
% 0.14/0.40 (![X: $i] : (cUnsatisfiable(X) => cdxcomp(X)) <=> ![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.14/0.40 tff(49,axiom,(![X: $i] : (cUnsatisfiable(X) => cdxcomp(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_2')).
% 0.14/0.40 tff(50,plain,
% 0.14/0.40 (![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.14/0.40 tff(51,plain,
% 0.14/0.40 (![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.14/0.40 tff(52,plain,(
% 0.14/0.40 ![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[51])).
% 0.14/0.40 tff(53,plain,
% 0.14/0.40 (![X: $i] : (cdxcomp(X) | (~cUnsatisfiable(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.14/0.40 tff(54,plain,
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% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(55,plain,
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% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(56,plain,
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% 0.14/0.40 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.14/0.40 tff(57,plain,
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% 0.14/0.40 inference(unit_resolution,[status(thm)],[56, 53, 43])).
% 0.14/0.40 tff(58,plain,
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% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(59,plain,
% 0.14/0.40 ((~((~cdxcomp(i2003_11_14_17_20_53634)) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))) | ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.14/0.40 tff(60,plain,
% 0.14/0.40 (ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[59, 40])).
% 0.14/0.40 tff(61,plain,
% 0.14/0.40 ((~![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))) | (~ra_Px1(i2003_11_14_17_20_53634, tptp_fun_Y0_1(i2003_11_14_17_20_53634)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(62,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[61, 60, 23])).
% 0.14/0.40 tff(63,plain,(~![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(64,plain,
% 0.14/0.40 ((~((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y)))) | (~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y))),
% 0.14/0.40 inference(tautology,[status(thm)],[])).
% 0.14/0.40 tff(65,plain,
% 0.14/0.40 ((~((~cd(i2003_11_14_17_20_53634)) | ![Y: $i] : (~ra_Px1(i2003_11_14_17_20_53634, Y)))) | (~cd(i2003_11_14_17_20_53634))),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.14/0.40 tff(66,plain,
% 0.14/0.40 (~cd(i2003_11_14_17_20_53634)),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[65, 22])).
% 0.14/0.40 tff(67,assumption,(ca_Ax2(i2003_11_14_17_20_53634)), introduced(assumption)).
% 0.14/0.40 tff(68,plain,
% 0.14/0.40 (^[X: $i] : refl((cd(X) | (~ca_Ax2(X))) <=> (cd(X) | (~ca_Ax2(X))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(69,plain,
% 0.14/0.40 (![X: $i] : (cd(X) | (~ca_Ax2(X))) <=> ![X: $i] : (cd(X) | (~ca_Ax2(X)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.14/0.40 tff(70,plain,
% 0.14/0.40 (![X: $i] : (cd(X) | (~ca_Ax2(X))) <=> ![X: $i] : (cd(X) | (~ca_Ax2(X)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(71,plain,
% 0.14/0.40 (^[X: $i] : rewrite((ca_Ax2(X) => cd(X)) <=> (cd(X) | (~ca_Ax2(X))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(72,plain,
% 0.14/0.40 (![X: $i] : (ca_Ax2(X) => cd(X)) <=> ![X: $i] : (cd(X) | (~ca_Ax2(X)))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.14/0.40 tff(73,axiom,(![X: $i] : (ca_Ax2(X) => cd(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_8')).
% 0.14/0.40 tff(74,plain,
% 0.14/0.40 (![X: $i] : (cd(X) | (~ca_Ax2(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.14/0.40 tff(75,plain,
% 0.14/0.40 (![X: $i] : (cd(X) | (~ca_Ax2(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.14/0.40 tff(76,plain,(
% 0.14/0.40 ![X: $i] : (cd(X) | (~ca_Ax2(X)))),
% 0.14/0.40 inference(skolemize,[status(sab)],[75])).
% 0.14/0.40 tff(77,plain,
% 0.14/0.40 (![X: $i] : (cd(X) | (~ca_Ax2(X)))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.14/0.40 tff(78,plain,
% 0.14/0.40 (((~![X: $i] : (cd(X) | (~ca_Ax2(X)))) | (cd(i2003_11_14_17_20_53634) | (~ca_Ax2(i2003_11_14_17_20_53634)))) <=> ((~![X: $i] : (cd(X) | (~ca_Ax2(X)))) | cd(i2003_11_14_17_20_53634) | (~ca_Ax2(i2003_11_14_17_20_53634)))),
% 0.14/0.40 inference(rewrite,[status(thm)],[])).
% 0.14/0.40 tff(79,plain,
% 0.14/0.40 ((~![X: $i] : (cd(X) | (~ca_Ax2(X)))) | (cd(i2003_11_14_17_20_53634) | (~ca_Ax2(i2003_11_14_17_20_53634)))),
% 0.14/0.40 inference(quant_inst,[status(thm)],[])).
% 0.14/0.40 tff(80,plain,
% 0.14/0.40 ((~![X: $i] : (cd(X) | (~ca_Ax2(X)))) | cd(i2003_11_14_17_20_53634) | (~ca_Ax2(i2003_11_14_17_20_53634))),
% 0.14/0.40 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.14/0.40 tff(81,plain,
% 0.14/0.40 ($false),
% 0.14/0.40 inference(unit_resolution,[status(thm)],[80, 77, 67, 66])).
% 0.14/0.40 tff(82,plain,(~ca_Ax2(i2003_11_14_17_20_53634)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.40 tff(83,plain,
% 0.14/0.40 (^[X: $i] : refl((~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X))))))))) <=> (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X))))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(84,plain,
% 0.14/0.40 (![X: $i] : (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X))))))))) <=> ![X: $i] : (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X)))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.14/0.40 tff(85,plain,
% 0.14/0.40 (^[X: $i] : rewrite((~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X))))))))) <=> (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X))))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(86,plain,
% 0.14/0.40 (![X: $i] : (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X))))))))) <=> ![X: $i] : (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X)))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[85])).
% 0.14/0.40 tff(87,plain,
% 0.14/0.40 (![X: $i] : (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X))))))))) <=> ![X: $i] : (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X)))))))))),
% 0.14/0.40 inference(transitivity,[status(thm)],[86, 84])).
% 0.14/0.40 tff(88,plain,
% 0.14/0.40 (^[X: $i] : trans(monotonicity(rewrite(((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))), ((((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X))))))) <=> (((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X))))))))), rewrite((((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X))))))) <=> (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X)))))))))), ((((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X))))))) <=> (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X)))))))))))),
% 0.14/0.40 inference(bind,[status(th)],[])).
% 0.14/0.40 tff(89,plain,
% 0.14/0.40 (![X: $i] : (((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X))))))) <=> ![X: $i] : (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X)))))))))),
% 0.14/0.40 inference(quant_intro,[status(thm)],[88])).
% 0.14/0.40 tff(90,plain,
% 0.14/0.40 (![X: $i] : (ca_Ax2(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ![X: $i] : (ca_Ax2(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(91,plain,
% 0.14/0.41 (^[X: $i] : rewrite((ca_Ax2(X) <=> ![Y: $i] : (rr(X, Y) => cc(Y))) <=> (ca_Ax2(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y)))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(92,plain,
% 0.14/0.41 (![X: $i] : (ca_Ax2(X) <=> ![Y: $i] : (rr(X, Y) => cc(Y))) <=> ![X: $i] : (ca_Ax2(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[91])).
% 0.14/0.41 tff(93,axiom,(![X: $i] : (ca_Ax2(X) <=> ![Y: $i] : (rr(X, Y) => cc(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_7')).
% 0.14/0.41 tff(94,plain,
% 0.14/0.41 (![X: $i] : (ca_Ax2(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.14/0.41 tff(95,plain,
% 0.14/0.41 (![X: $i] : (ca_Ax2(X) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.14/0.41 tff(96,plain,(
% 0.14/0.41 ![X: $i] : (((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) & (ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X)))))))),
% 0.14/0.41 inference(skolemize,[status(sab)],[95])).
% 0.14/0.41 tff(97,plain,
% 0.14/0.41 (![X: $i] : (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X)))))))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.14/0.41 tff(98,plain,
% 0.14/0.41 (![X: $i] : (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X)))))))))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[97, 87])).
% 0.14/0.41 tff(99,plain,
% 0.14/0.41 ((~![X: $i] : (~((~((~ca_Ax2(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~(ca_Ax2(X) | (~(cc(tptp_fun_Y_2(X)) | (~rr(X, tptp_fun_Y_2(X)))))))))) | (~((~((~ca_Ax2(i2003_11_14_17_20_53634)) | ![Y: $i] : (cc(Y) | (~rr(i2003_11_14_17_20_53634, Y))))) | (~(ca_Ax2(i2003_11_14_17_20_53634) | (~(cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634)))))))))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(100,plain,
% 0.14/0.41 (~((~((~ca_Ax2(i2003_11_14_17_20_53634)) | ![Y: $i] : (cc(Y) | (~rr(i2003_11_14_17_20_53634, Y))))) | (~(ca_Ax2(i2003_11_14_17_20_53634) | (~(cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634))))))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.14/0.41 tff(101,plain,
% 0.14/0.41 (((~((~ca_Ax2(i2003_11_14_17_20_53634)) | ![Y: $i] : (cc(Y) | (~rr(i2003_11_14_17_20_53634, Y))))) | (~(ca_Ax2(i2003_11_14_17_20_53634) | (~(cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634)))))))) | (ca_Ax2(i2003_11_14_17_20_53634) | (~(cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634))))))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(102,plain,
% 0.14/0.41 (ca_Ax2(i2003_11_14_17_20_53634) | (~(cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634)))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.14/0.41 tff(103,plain,
% 0.14/0.41 ((~(ca_Ax2(i2003_11_14_17_20_53634) | (~(cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634))))))) | ca_Ax2(i2003_11_14_17_20_53634) | (~(cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634)))))),
% 0.14/0.41 inference(tautology,[status(thm)],[])).
% 0.14/0.41 tff(104,plain,
% 0.14/0.41 (ca_Ax2(i2003_11_14_17_20_53634) | (~(cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634)))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.14/0.41 tff(105,plain,
% 0.14/0.41 (~(cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634))))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[104, 82])).
% 0.14/0.41 tff(106,plain,
% 0.14/0.41 ((cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634)))) | rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(107,plain,
% 0.21/0.41 (rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.21/0.41 tff(108,plain,
% 0.21/0.41 ((cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634)))) | (~cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(109,plain,
% 0.21/0.41 (~cc(tptp_fun_Y_2(i2003_11_14_17_20_53634))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[108, 105])).
% 0.21/0.41 tff(110,plain,
% 0.21/0.41 (^[X: $i] : refl((cc(X) | (~cUnsatisfiable(X))) <=> (cc(X) | (~cUnsatisfiable(X))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(111,plain,
% 0.21/0.41 (![X: $i] : (cc(X) | (~cUnsatisfiable(X))) <=> ![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[110])).
% 0.21/0.41 tff(112,plain,
% 0.21/0.41 (![X: $i] : (cc(X) | (~cUnsatisfiable(X))) <=> ![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(113,plain,
% 0.21/0.41 (^[X: $i] : rewrite((cUnsatisfiable(X) => cc(X)) <=> (cc(X) | (~cUnsatisfiable(X))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(114,plain,
% 0.21/0.41 (![X: $i] : (cUnsatisfiable(X) => cc(X)) <=> ![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.41 tff(115,axiom,(![X: $i] : (cUnsatisfiable(X) => cc(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_3')).
% 0.21/0.41 tff(116,plain,
% 0.21/0.41 (![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.21/0.41 tff(117,plain,
% 0.21/0.41 (![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.21/0.41 tff(118,plain,(
% 0.21/0.41 ![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[117])).
% 0.21/0.41 tff(119,plain,
% 0.21/0.41 (![X: $i] : (cc(X) | (~cUnsatisfiable(X)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[118, 111])).
% 0.21/0.41 tff(120,plain,
% 0.21/0.41 (((~![X: $i] : (cc(X) | (~cUnsatisfiable(X)))) | (cc(i2003_11_14_17_20_53634) | (~cUnsatisfiable(i2003_11_14_17_20_53634)))) <=> ((~![X: $i] : (cc(X) | (~cUnsatisfiable(X)))) | cc(i2003_11_14_17_20_53634) | (~cUnsatisfiable(i2003_11_14_17_20_53634)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(121,plain,
% 0.21/0.41 ((~![X: $i] : (cc(X) | (~cUnsatisfiable(X)))) | (cc(i2003_11_14_17_20_53634) | (~cUnsatisfiable(i2003_11_14_17_20_53634)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(122,plain,
% 0.21/0.41 ((~![X: $i] : (cc(X) | (~cUnsatisfiable(X)))) | cc(i2003_11_14_17_20_53634) | (~cUnsatisfiable(i2003_11_14_17_20_53634))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.41 tff(123,plain,
% 0.21/0.41 (cc(i2003_11_14_17_20_53634)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[122, 119, 43])).
% 0.21/0.41 tff(124,plain,
% 0.21/0.41 (^[X: $i] : refl(((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(125,plain,
% 0.21/0.41 (![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[124])).
% 0.21/0.41 tff(126,plain,
% 0.21/0.41 (^[X: $i] : rewrite(((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(127,plain,
% 0.21/0.41 (![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[126])).
% 0.21/0.41 tff(128,plain,
% 0.21/0.41 (![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[127, 125])).
% 0.21/0.41 tff(129,plain,
% 0.21/0.41 (![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(130,plain,
% 0.21/0.41 (^[X: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite((rr(X, Y) => cc(Y)) <=> (cc(Y) | (~rr(X, Y))))), (![Y: $i] : (rr(X, Y) => cc(Y)) <=> ![Y: $i] : (cc(Y) | (~rr(X, Y))))), ((cc(X) => ![Y: $i] : (rr(X, Y) => cc(Y))) <=> (cc(X) => ![Y: $i] : (cc(Y) | (~rr(X, Y)))))), rewrite((cc(X) => ![Y: $i] : (cc(Y) | (~rr(X, Y)))) <=> ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))), ((cc(X) => ![Y: $i] : (rr(X, Y) => cc(Y))) <=> ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(131,plain,
% 0.21/0.42 (![X: $i] : (cc(X) => ![Y: $i] : (rr(X, Y) => cc(Y))) <=> ![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[130])).
% 0.21/0.42 tff(132,axiom,(![X: $i] : (cc(X) => ![Y: $i] : (rr(X, Y) => cc(Y)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_4')).
% 0.21/0.42 tff(133,plain,
% 0.21/0.42 (![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.21/0.42 tff(134,plain,
% 0.21/0.42 (![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.21/0.42 tff(135,plain,(
% 0.21/0.42 ![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[134])).
% 0.21/0.42 tff(136,plain,
% 0.21/0.42 (![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[135, 128])).
% 0.21/0.42 tff(137,plain,
% 0.21/0.42 (((~![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | ((~cc(i2003_11_14_17_20_53634)) | ![Y: $i] : (cc(Y) | (~rr(i2003_11_14_17_20_53634, Y))))) <=> ((~![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~cc(i2003_11_14_17_20_53634)) | ![Y: $i] : (cc(Y) | (~rr(i2003_11_14_17_20_53634, Y))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(138,plain,
% 0.21/0.42 ((~![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | ((~cc(i2003_11_14_17_20_53634)) | ![Y: $i] : (cc(Y) | (~rr(i2003_11_14_17_20_53634, Y))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(139,plain,
% 0.21/0.42 ((~![X: $i] : ((~cc(X)) | ![Y: $i] : (cc(Y) | (~rr(X, Y))))) | (~cc(i2003_11_14_17_20_53634)) | ![Y: $i] : (cc(Y) | (~rr(i2003_11_14_17_20_53634, Y)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.21/0.42 tff(140,plain,
% 0.21/0.42 (![Y: $i] : (cc(Y) | (~rr(i2003_11_14_17_20_53634, Y)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[139, 136, 123])).
% 0.21/0.42 tff(141,plain,
% 0.21/0.42 (((~![Y: $i] : (cc(Y) | (~rr(i2003_11_14_17_20_53634, Y)))) | (cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634))))) <=> ((~![Y: $i] : (cc(Y) | (~rr(i2003_11_14_17_20_53634, Y)))) | cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(142,plain,
% 0.21/0.42 ((~![Y: $i] : (cc(Y) | (~rr(i2003_11_14_17_20_53634, Y)))) | (cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(143,plain,
% 0.21/0.42 ((~![Y: $i] : (cc(Y) | (~rr(i2003_11_14_17_20_53634, Y)))) | cc(tptp_fun_Y_2(i2003_11_14_17_20_53634)) | (~rr(i2003_11_14_17_20_53634, tptp_fun_Y_2(i2003_11_14_17_20_53634)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.21/0.42 tff(144,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[143, 140, 109, 107])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------