TSTP Solution File: SYN323-1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN323-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n025.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 23:54:42 EDT 2022

% Result   : Unsatisfiable 0.13s 0.39s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYN323-1 : TPTP v8.1.0. Released v1.2.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n025.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 02:42:34 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.
% 0.13/0.39  % SZS status Unsatisfiable
% 0.13/0.39  % SZS output start Proof
% 0.13/0.39  tff(g_type, type, (
% 0.13/0.39     g: ( $i * $i ) > $o)).
% 0.13/0.39  tff(a_type, type, (
% 0.13/0.39     a: $i)).
% 0.13/0.39  tff(f_type, type, (
% 0.13/0.39     f: ( $i * $i ) > $o)).
% 0.13/0.39  tff(1,assumption,(~g(a, a)), introduced(assumption)).
% 0.13/0.39  tff(2,plain,
% 0.13/0.39      (^[X: $i] : refl((f(X, a) | g(X, a)) <=> (f(X, a) | g(X, a)))),
% 0.13/0.39      inference(bind,[status(th)],[])).
% 0.13/0.39  tff(3,plain,
% 0.13/0.39      (![X: $i] : (f(X, a) | g(X, a)) <=> ![X: $i] : (f(X, a) | g(X, a))),
% 0.13/0.39      inference(quant_intro,[status(thm)],[2])).
% 0.13/0.39  tff(4,plain,
% 0.13/0.39      (![X: $i] : (f(X, a) | g(X, a)) <=> ![X: $i] : (f(X, a) | g(X, a))),
% 0.13/0.39      inference(rewrite,[status(thm)],[])).
% 0.13/0.39  tff(5,axiom,(![X: $i] : (f(X, a) | g(X, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause1')).
% 0.13/0.39  tff(6,plain,
% 0.13/0.39      (![X: $i] : (f(X, a) | g(X, a))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[5, 4])).
% 0.13/0.39  tff(7,plain,(
% 0.13/0.39      ![X: $i] : (f(X, a) | g(X, a))),
% 0.13/0.39      inference(skolemize,[status(sab)],[6])).
% 0.13/0.39  tff(8,plain,
% 0.13/0.39      (![X: $i] : (f(X, a) | g(X, a))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.39  tff(9,plain,
% 0.13/0.39      (((~![X: $i] : (f(X, a) | g(X, a))) | (f(a, a) | g(a, a))) <=> ((~![X: $i] : (f(X, a) | g(X, a))) | f(a, a) | g(a, a))),
% 0.13/0.39      inference(rewrite,[status(thm)],[])).
% 0.13/0.39  tff(10,plain,
% 0.13/0.39      ((~![X: $i] : (f(X, a) | g(X, a))) | (f(a, a) | g(a, a))),
% 0.13/0.39      inference(quant_inst,[status(thm)],[])).
% 0.13/0.39  tff(11,plain,
% 0.13/0.39      ((~![X: $i] : (f(X, a) | g(X, a))) | f(a, a) | g(a, a)),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[10, 9])).
% 0.13/0.39  tff(12,plain,
% 0.13/0.39      (f(a, a) | g(a, a)),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[11, 8])).
% 0.13/0.39  tff(13,plain,
% 0.13/0.39      (f(a, a)),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[12, 1])).
% 0.13/0.39  tff(14,plain,
% 0.13/0.39      (^[X: $i] : refl(((~f(a, X)) | g(X, a)) <=> ((~f(a, X)) | g(X, a)))),
% 0.13/0.39      inference(bind,[status(th)],[])).
% 0.13/0.39  tff(15,plain,
% 0.13/0.39      (![X: $i] : ((~f(a, X)) | g(X, a)) <=> ![X: $i] : ((~f(a, X)) | g(X, a))),
% 0.13/0.39      inference(quant_intro,[status(thm)],[14])).
% 0.13/0.39  tff(16,plain,
% 0.13/0.39      (![X: $i] : ((~f(a, X)) | g(X, a)) <=> ![X: $i] : ((~f(a, X)) | g(X, a))),
% 0.13/0.39      inference(rewrite,[status(thm)],[])).
% 0.13/0.39  tff(17,axiom,(![X: $i] : ((~f(a, X)) | g(X, a))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause2')).
% 0.13/0.39  tff(18,plain,
% 0.13/0.39      (![X: $i] : ((~f(a, X)) | g(X, a))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[17, 16])).
% 0.13/0.39  tff(19,plain,(
% 0.13/0.39      ![X: $i] : ((~f(a, X)) | g(X, a))),
% 0.13/0.39      inference(skolemize,[status(sab)],[18])).
% 0.13/0.39  tff(20,plain,
% 0.13/0.39      (![X: $i] : ((~f(a, X)) | g(X, a))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[19, 15])).
% 0.13/0.39  tff(21,plain,
% 0.13/0.39      (((~![X: $i] : ((~f(a, X)) | g(X, a))) | ((~f(a, a)) | g(a, a))) <=> ((~![X: $i] : ((~f(a, X)) | g(X, a))) | (~f(a, a)) | g(a, a))),
% 0.13/0.39      inference(rewrite,[status(thm)],[])).
% 0.13/0.39  tff(22,plain,
% 0.13/0.39      ((~![X: $i] : ((~f(a, X)) | g(X, a))) | ((~f(a, a)) | g(a, a))),
% 0.13/0.39      inference(quant_inst,[status(thm)],[])).
% 0.13/0.39  tff(23,plain,
% 0.13/0.39      ((~![X: $i] : ((~f(a, X)) | g(X, a))) | (~f(a, a)) | g(a, a)),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[22, 21])).
% 0.13/0.39  tff(24,plain,
% 0.13/0.39      ($false),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[23, 20, 13, 1])).
% 0.13/0.39  tff(25,plain,(g(a, a)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39  tff(26,plain,
% 0.13/0.39      (^[X: $i] : refl(((~f(a, X)) | (~g(X, a))) <=> ((~f(a, X)) | (~g(X, a))))),
% 0.13/0.39      inference(bind,[status(th)],[])).
% 0.13/0.39  tff(27,plain,
% 0.13/0.39      (![X: $i] : ((~f(a, X)) | (~g(X, a))) <=> ![X: $i] : ((~f(a, X)) | (~g(X, a)))),
% 0.13/0.39      inference(quant_intro,[status(thm)],[26])).
% 0.13/0.39  tff(28,plain,
% 0.13/0.39      (![X: $i] : ((~f(a, X)) | (~g(X, a))) <=> ![X: $i] : ((~f(a, X)) | (~g(X, a)))),
% 0.13/0.39      inference(rewrite,[status(thm)],[])).
% 0.13/0.39  tff(29,axiom,(![X: $i] : ((~f(a, X)) | (~g(X, a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause4')).
% 0.13/0.39  tff(30,plain,
% 0.13/0.39      (![X: $i] : ((~f(a, X)) | (~g(X, a)))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[29, 28])).
% 0.13/0.39  tff(31,plain,(
% 0.13/0.39      ![X: $i] : ((~f(a, X)) | (~g(X, a)))),
% 0.13/0.39      inference(skolemize,[status(sab)],[30])).
% 0.13/0.39  tff(32,plain,
% 0.13/0.39      (![X: $i] : ((~f(a, X)) | (~g(X, a)))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[31, 27])).
% 0.13/0.39  tff(33,plain,
% 0.13/0.39      (((~![X: $i] : ((~f(a, X)) | (~g(X, a)))) | ((~f(a, a)) | (~g(a, a)))) <=> ((~![X: $i] : ((~f(a, X)) | (~g(X, a)))) | (~f(a, a)) | (~g(a, a)))),
% 0.13/0.39      inference(rewrite,[status(thm)],[])).
% 0.13/0.39  tff(34,plain,
% 0.13/0.39      ((~![X: $i] : ((~f(a, X)) | (~g(X, a)))) | ((~f(a, a)) | (~g(a, a)))),
% 0.13/0.39      inference(quant_inst,[status(thm)],[])).
% 0.13/0.39  tff(35,plain,
% 0.13/0.39      ((~![X: $i] : ((~f(a, X)) | (~g(X, a)))) | (~f(a, a)) | (~g(a, a))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[34, 33])).
% 0.13/0.39  tff(36,plain,
% 0.13/0.39      (~f(a, a)),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[35, 32, 25])).
% 0.13/0.39  tff(37,plain,
% 0.13/0.39      (^[X: $i] : refl((f(X, a) | (~g(X, a))) <=> (f(X, a) | (~g(X, a))))),
% 0.13/0.39      inference(bind,[status(th)],[])).
% 0.13/0.39  tff(38,plain,
% 0.13/0.39      (![X: $i] : (f(X, a) | (~g(X, a))) <=> ![X: $i] : (f(X, a) | (~g(X, a)))),
% 0.13/0.39      inference(quant_intro,[status(thm)],[37])).
% 0.13/0.39  tff(39,plain,
% 0.13/0.39      (![X: $i] : (f(X, a) | (~g(X, a))) <=> ![X: $i] : (f(X, a) | (~g(X, a)))),
% 0.13/0.39      inference(rewrite,[status(thm)],[])).
% 0.13/0.39  tff(40,axiom,(![X: $i] : (f(X, a) | (~g(X, a)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause3')).
% 0.13/0.39  tff(41,plain,
% 0.13/0.39      (![X: $i] : (f(X, a) | (~g(X, a)))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[40, 39])).
% 0.13/0.39  tff(42,plain,(
% 0.13/0.39      ![X: $i] : (f(X, a) | (~g(X, a)))),
% 0.13/0.39      inference(skolemize,[status(sab)],[41])).
% 0.13/0.39  tff(43,plain,
% 0.13/0.39      (![X: $i] : (f(X, a) | (~g(X, a)))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[42, 38])).
% 0.13/0.39  tff(44,plain,
% 0.13/0.39      (((~![X: $i] : (f(X, a) | (~g(X, a)))) | (f(a, a) | (~g(a, a)))) <=> ((~![X: $i] : (f(X, a) | (~g(X, a)))) | f(a, a) | (~g(a, a)))),
% 0.13/0.39      inference(rewrite,[status(thm)],[])).
% 0.13/0.39  tff(45,plain,
% 0.13/0.39      ((~![X: $i] : (f(X, a) | (~g(X, a)))) | (f(a, a) | (~g(a, a)))),
% 0.13/0.39      inference(quant_inst,[status(thm)],[])).
% 0.13/0.39  tff(46,plain,
% 0.13/0.39      ((~![X: $i] : (f(X, a) | (~g(X, a)))) | f(a, a) | (~g(a, a))),
% 0.13/0.39      inference(modus_ponens,[status(thm)],[45, 44])).
% 0.13/0.39  tff(47,plain,
% 0.13/0.39      ($false),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[46, 43, 36, 25])).
% 0.13/0.39  % SZS output end Proof
%------------------------------------------------------------------------------