TSTP Solution File: ITP353_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 04:18:49 EDT 2022
% Result : Theorem 0.56s 0.69s
% Output : Proof 0.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n029.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 07:37:13 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.
% 0.56/0.69 % SZS status Theorem
% 0.56/0.69 % SZS output start Proof
% 0.56/0.69 tff(tptp_fun__inverse_a__type, type, (
% 0.56/0.69 tptp_fun__inverse_a_: 'Ereal$' > 'Ereal$')).
% 0.56/0.69 tff(tptp_fun__ereal___type, type, (
% 0.56/0.69 tptp_fun__ereal__: $real > 'Ereal$')).
% 0.56/0.69 tff(tptp_fun__c___type, type, (
% 0.56/0.69 tptp_fun__c__: $real)).
% 0.56/0.69 tff(tptp_fun__fun_app_c__type, type, (
% 0.56/0.69 tptp_fun__fun_app_c_: ( 'Real_real_fun$' * $real ) > $real)).
% 0.56/0.69 tff(tptp_fun__inverse___type, type, (
% 0.56/0.69 tptp_fun__inverse__: 'Real_real_fun$')).
% 0.56/0.69 tff(tptp_fun__infinity___type, type, (
% 0.56/0.69 tptp_fun__infinity__: 'Ereal$')).
% 0.56/0.69 tff(1,plain,
% 0.56/0.69 (^[A__questionmark_v0: $real] : refl((~((~((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|))) | (~((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0))))))) <=> (~((~((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|))) | (~((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0))))))))),
% 0.56/0.69 inference(bind,[status(th)],[])).
% 0.56/0.69 tff(2,plain,
% 0.56/0.69 (![A__questionmark_v0: $real] : (~((~((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|))) | (~((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0))))))) <=> ![A__questionmark_v0: $real] : (~((~((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|))) | (~((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0)))))))),
% 0.56/0.69 inference(quant_intro,[status(thm)],[1])).
% 0.56/0.69 tff(3,plain,
% 0.56/0.69 (^[A__questionmark_v0: $real] : rewrite((((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|)) & ((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0))))) <=> (~((~((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|))) | (~((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0))))))))),
% 0.56/0.69 inference(bind,[status(th)],[])).
% 0.56/0.69 tff(4,plain,
% 0.56/0.69 (![A__questionmark_v0: $real] : (((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|)) & ((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0))))) <=> ![A__questionmark_v0: $real] : (~((~((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|))) | (~((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0)))))))),
% 0.56/0.69 inference(quant_intro,[status(thm)],[3])).
% 0.56/0.69 tff(5,plain,
% 0.56/0.69 (![A__questionmark_v0: $real] : (((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|)) & ((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0))))) <=> ![A__questionmark_v0: $real] : (((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|)) & ((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0)))))),
% 0.56/0.69 inference(rewrite,[status(thm)],[])).
% 0.56/0.69 tff(6,plain,
% 0.56/0.69 (^[A__questionmark_v0: $real] : rewrite((((A__questionmark_v0 = 0) => (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|)) & ((~(A__questionmark_v0 = 0)) => (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0))))) <=> (((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|)) & ((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0))))))),
% 0.56/0.69 inference(bind,[status(th)],[])).
% 0.56/0.69 tff(7,plain,
% 0.56/0.69 (![A__questionmark_v0: $real] : (((A__questionmark_v0 = 0) => (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|)) & ((~(A__questionmark_v0 = 0)) => (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0))))) <=> ![A__questionmark_v0: $real] : (((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|)) & ((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0)))))),
% 0.56/0.69 inference(quant_intro,[status(thm)],[6])).
% 0.56/0.69 tff(8,axiom,(![A__questionmark_v0: $real] : (((A__questionmark_v0 = 0) => (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|)) & ((~(A__questionmark_v0 = 0)) => (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom19')).
% 0.56/0.69 tff(9,plain,
% 0.56/0.69 (![A__questionmark_v0: $real] : (((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|)) & ((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0)))))),
% 0.56/0.69 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.56/0.69 tff(10,plain,
% 0.56/0.69 (![A__questionmark_v0: $real] : (((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|)) & ((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0)))))),
% 0.56/0.69 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.56/0.69 tff(11,plain,(
% 0.56/0.69 ![A__questionmark_v0: $real] : (((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|)) & ((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0)))))),
% 0.56/0.69 inference(skolemize,[status(sab)],[10])).
% 0.56/0.69 tff(12,plain,
% 0.56/0.69 (![A__questionmark_v0: $real] : (~((~((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|))) | (~((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0)))))))),
% 0.56/0.69 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.56/0.69 tff(13,plain,
% 0.56/0.69 (![A__questionmark_v0: $real] : (~((~((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|))) | (~((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0)))))))),
% 0.56/0.69 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.56/0.69 tff(14,plain,
% 0.56/0.69 ((~![A__questionmark_v0: $real] : (~((~((~(A__questionmark_v0 = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = |'infinity$'|))) | (~((A__questionmark_v0 = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(A__questionmark_v0)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, A__questionmark_v0)))))))) | (~((~((~(|'c$'| = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = |'infinity$'|))) | (~((|'c$'| = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|)))))))),
% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
% 0.68/0.72 tff(15,plain,
% 0.68/0.72 (~((~((~(|'c$'| = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = |'infinity$'|))) | (~((|'c$'| = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|))))))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.68/0.72 tff(16,plain,
% 0.68/0.72 (((~((~(|'c$'| = 0)) | (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = |'infinity$'|))) | (~((|'c$'| = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|)))))) | ((|'c$'| = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|))))),
% 0.68/0.72 inference(tautology,[status(thm)],[])).
% 0.68/0.72 tff(17,plain,
% 0.68/0.72 ((|'c$'| = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|)))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.68/0.72 tff(18,plain,
% 0.68/0.72 ((~$lesseq(|'c$'|, 0)) <=> (~$lesseq(|'c$'|, 0))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(19,plain,
% 0.68/0.72 ($less(0, |'c$'|) <=> (~$lesseq(|'c$'|, 0))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(20,axiom,($less(0, |'c$'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom5')).
% 0.68/0.72 tff(21,plain,
% 0.68/0.72 (~$lesseq(|'c$'|, 0)),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.68/0.72 tff(22,plain,
% 0.68/0.72 (~$lesseq(|'c$'|, 0)),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.68/0.72 tff(23,plain,
% 0.68/0.72 ((~(|'c$'| = 0)) | $lesseq(|'c$'|, 0)),
% 0.68/0.72 inference(theory_lemma,[status(thm)],[])).
% 0.68/0.72 tff(24,plain,
% 0.68/0.72 (~(|'c$'| = 0)),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.68/0.72 tff(25,plain,
% 0.68/0.72 ((~((|'c$'| = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|))))) | (|'c$'| = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|)))),
% 0.68/0.72 inference(tautology,[status(thm)],[])).
% 0.68/0.72 tff(26,plain,
% 0.68/0.72 ((~((|'c$'| = 0) | (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|))))) | (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|)))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.68/0.72 tff(27,plain,
% 0.68/0.72 (tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)) = tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|))),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[26, 17])).
% 0.68/0.72 tff(28,plain,
% 0.68/0.72 (tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|)) = tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|))),
% 0.68/0.72 inference(symmetry,[status(thm)],[27])).
% 0.68/0.72 tff(29,plain,
% 0.68/0.72 ((~(tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|)) = tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)))) <=> (~(tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|)) = tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|))))),
% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(30,axiom,(~(tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|)) = tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture3')).
% 0.68/0.72 tff(31,plain,
% 0.68/0.72 (~(tptp_fun__ereal__(tptp_fun__fun_app_c_(|'inverse$'|, |'c$'|)) = tptp_fun__inverse_a_(tptp_fun__ereal__(|'c$'|)))),
% 0.68/0.72 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.68/0.72 tff(32,plain,
% 0.68/0.72 ($false),
% 0.68/0.72 inference(unit_resolution,[status(thm)],[31, 28])).
% 0.68/0.72 % SZS output end Proof
%------------------------------------------------------------------------------