TSTP Solution File: SYN081+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN081+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n002.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 23:53:39 EDT 2022

% Result   : Theorem 0.21s 0.39s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SYN081+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n002.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Sep  5 01:52:48 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.21/0.39  % SZS status Theorem
% 0.21/0.39  % SZS output start Proof
% 0.21/0.39  tff(big_f_type, type, (
% 0.21/0.39     big_f: $i > $o)).
% 0.21/0.39  tff(f_type, type, (
% 0.21/0.39     f: $i > $i)).
% 0.21/0.39  tff(elem_0_type, type, (
% 0.21/0.39     elem_0: $i)).
% 0.21/0.39  tff(1,assumption,(big_f(f(elem!0))), introduced(assumption)).
% 0.21/0.39  tff(2,plain,
% 0.21/0.39      (^[X: $i] : refl((big_f(f(X)) | (~big_f(X))) <=> (big_f(f(X)) | (~big_f(X))))),
% 0.21/0.39      inference(bind,[status(th)],[])).
% 0.21/0.39  tff(3,plain,
% 0.21/0.39      (![X: $i] : (big_f(f(X)) | (~big_f(X))) <=> ![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.21/0.39      inference(quant_intro,[status(thm)],[2])).
% 0.21/0.39  tff(4,plain,
% 0.21/0.39      (^[X: $i] : trans(monotonicity(rewrite((big_f(X) & (~big_f(f(X)))) <=> (~(big_f(f(X)) | (~big_f(X))))), ((~(big_f(X) & (~big_f(f(X))))) <=> (~(~(big_f(f(X)) | (~big_f(X))))))), rewrite((~(~(big_f(f(X)) | (~big_f(X))))) <=> (big_f(f(X)) | (~big_f(X)))), ((~(big_f(X) & (~big_f(f(X))))) <=> (big_f(f(X)) | (~big_f(X)))))),
% 0.21/0.39      inference(bind,[status(th)],[])).
% 0.21/0.39  tff(5,plain,
% 0.21/0.39      (![X: $i] : (~(big_f(X) & (~big_f(f(X))))) <=> ![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.21/0.39      inference(quant_intro,[status(thm)],[4])).
% 0.21/0.39  tff(6,plain,
% 0.21/0.39      ((~?[X: $i] : (big_f(X) & (~big_f(f(X))))) <=> (~?[X: $i] : (big_f(X) & (~big_f(f(X)))))),
% 0.21/0.39      inference(rewrite,[status(thm)],[])).
% 0.21/0.39  tff(7,axiom,(~?[X: $i] : (big_f(X) & (~big_f(f(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel59')).
% 0.21/0.39  tff(8,plain,
% 0.21/0.39      (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[7, 6])).
% 0.21/0.39  tff(9,plain,
% 0.21/0.39      (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[8, 6])).
% 0.21/0.39  tff(10,plain,
% 0.21/0.39      (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[9, 6])).
% 0.21/0.39  tff(11,plain,
% 0.21/0.39      (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.39  tff(12,plain,
% 0.21/0.39      (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[11, 6])).
% 0.21/0.39  tff(13,plain,
% 0.21/0.39      (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[12, 6])).
% 0.21/0.39  tff(14,plain,
% 0.21/0.39      (~?[X: $i] : (big_f(X) & (~big_f(f(X))))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[13, 6])).
% 0.21/0.39  tff(15,plain,
% 0.21/0.39      (^[X: $i] : refl($oeq((~(big_f(X) & (~big_f(f(X))))), (~(big_f(X) & (~big_f(f(X)))))))),
% 0.21/0.39      inference(bind,[status(th)],[])).
% 0.21/0.39  tff(16,plain,(
% 0.21/0.39      ![X: $i] : (~(big_f(X) & (~big_f(f(X)))))),
% 0.21/0.39      inference(nnf-neg,[status(sab)],[14, 15])).
% 0.21/0.39  tff(17,plain,
% 0.21/0.39      (![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[16, 5])).
% 0.21/0.39  tff(18,plain,
% 0.21/0.39      (![X: $i] : (big_f(f(X)) | (~big_f(X)))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[17, 3])).
% 0.21/0.39  tff(19,plain,
% 0.21/0.39      (((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(f(elem!0))) | (~big_f(f(elem!0))))) <=> ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(f(elem!0))) | (~big_f(f(elem!0))))),
% 0.21/0.39      inference(rewrite,[status(thm)],[])).
% 0.21/0.39  tff(20,plain,
% 0.21/0.39      ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(f(elem!0))) | (~big_f(f(elem!0))))),
% 0.21/0.39      inference(quant_inst,[status(thm)],[])).
% 0.21/0.39  tff(21,plain,
% 0.21/0.39      ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(f(elem!0))) | (~big_f(f(elem!0)))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.39  tff(22,plain,
% 0.21/0.39      (big_f(f(f(elem!0))) | (~big_f(f(elem!0)))),
% 0.21/0.39      inference(unit_resolution,[status(thm)],[21, 18])).
% 0.21/0.39  tff(23,plain,
% 0.21/0.39      (big_f(f(f(elem!0)))),
% 0.21/0.39      inference(unit_resolution,[status(thm)],[22, 1])).
% 0.21/0.39  tff(24,assumption,(~(big_f(f(elem!0)) <=> (~big_f(f(f(elem!0)))))), introduced(assumption)).
% 0.21/0.39  tff(25,plain,
% 0.21/0.39      (^[X: $i] : refl((big_f(X) <=> (~big_f(f(X)))) <=> (big_f(X) <=> (~big_f(f(X)))))),
% 0.21/0.39      inference(bind,[status(th)],[])).
% 0.21/0.39  tff(26,plain,
% 0.21/0.39      (![X: $i] : (big_f(X) <=> (~big_f(f(X)))) <=> ![X: $i] : (big_f(X) <=> (~big_f(f(X))))),
% 0.21/0.39      inference(quant_intro,[status(thm)],[25])).
% 0.21/0.39  tff(27,plain,
% 0.21/0.39      (![X: $i] : (big_f(X) <=> (~big_f(f(X)))) <=> ![X: $i] : (big_f(X) <=> (~big_f(f(X))))),
% 0.21/0.39      inference(rewrite,[status(thm)],[])).
% 0.21/0.39  tff(28,axiom,(![X: $i] : (big_f(X) <=> (~big_f(f(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','pel59_1')).
% 0.21/0.39  tff(29,plain,
% 0.21/0.39      (![X: $i] : (big_f(X) <=> (~big_f(f(X))))),
% 0.21/0.39      inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.40  tff(30,plain,(
% 0.21/0.40      ![X: $i] : (big_f(X) <=> (~big_f(f(X))))),
% 0.21/0.40      inference(skolemize,[status(sab)],[29])).
% 0.21/0.40  tff(31,plain,
% 0.21/0.40      (![X: $i] : (big_f(X) <=> (~big_f(f(X))))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.40  tff(32,plain,
% 0.21/0.40      ((~![X: $i] : (big_f(X) <=> (~big_f(f(X))))) | (big_f(f(elem!0)) <=> (~big_f(f(f(elem!0)))))),
% 0.21/0.40      inference(quant_inst,[status(thm)],[])).
% 0.21/0.40  tff(33,plain,
% 0.21/0.40      ($false),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[32, 31, 24])).
% 0.21/0.40  tff(34,plain,(big_f(f(elem!0)) <=> (~big_f(f(f(elem!0))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40  tff(35,plain,
% 0.21/0.40      ((~(big_f(f(elem!0)) <=> (~big_f(f(f(elem!0)))))) | (~big_f(f(elem!0))) | (~big_f(f(f(elem!0))))),
% 0.21/0.40      inference(tautology,[status(thm)],[])).
% 0.21/0.40  tff(36,plain,
% 0.21/0.40      ((~big_f(f(elem!0))) | (~big_f(f(f(elem!0))))),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.40  tff(37,plain,
% 0.21/0.40      ($false),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[36, 23, 1])).
% 0.21/0.40  tff(38,plain,(~big_f(f(elem!0))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40  tff(39,plain,
% 0.21/0.40      ((~![X: $i] : (big_f(X) <=> (~big_f(f(X))))) | (big_f(elem!0) <=> (~big_f(f(elem!0))))),
% 0.21/0.40      inference(quant_inst,[status(thm)],[])).
% 0.21/0.40  tff(40,plain,
% 0.21/0.40      (big_f(elem!0) <=> (~big_f(f(elem!0)))),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[39, 31])).
% 0.21/0.40  tff(41,plain,
% 0.21/0.40      ((~(big_f(elem!0) <=> (~big_f(f(elem!0))))) | big_f(elem!0) | big_f(f(elem!0))),
% 0.21/0.40      inference(tautology,[status(thm)],[])).
% 0.21/0.40  tff(42,plain,
% 0.21/0.40      (big_f(elem!0) | big_f(f(elem!0))),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[41, 40])).
% 0.21/0.40  tff(43,plain,
% 0.21/0.40      (big_f(elem!0)),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[42, 38])).
% 0.21/0.40  tff(44,plain,
% 0.21/0.40      (((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(elem!0)) | (~big_f(elem!0)))) <=> ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(elem!0)) | (~big_f(elem!0)))),
% 0.21/0.40      inference(rewrite,[status(thm)],[])).
% 0.21/0.40  tff(45,plain,
% 0.21/0.40      ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | (big_f(f(elem!0)) | (~big_f(elem!0)))),
% 0.21/0.40      inference(quant_inst,[status(thm)],[])).
% 0.21/0.40  tff(46,plain,
% 0.21/0.40      ((~![X: $i] : (big_f(f(X)) | (~big_f(X)))) | big_f(f(elem!0)) | (~big_f(elem!0))),
% 0.21/0.40      inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.40  tff(47,plain,
% 0.21/0.40      (big_f(f(elem!0)) | (~big_f(elem!0))),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[46, 18])).
% 0.21/0.40  tff(48,plain,
% 0.21/0.40      ($false),
% 0.21/0.40      inference(unit_resolution,[status(thm)],[47, 43, 38])).
% 0.21/0.40  % SZS output end Proof
%------------------------------------------------------------------------------