TSTP Solution File: SYN405+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN405+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n006.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 23:55:11 EDT 2022

% Result   : Theorem 0.14s 0.39s
% Output   : Proof 0.14s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SYN405+1 : TPTP v8.1.0. Released v2.0.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34  % Computer : n006.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 : Mon Sep  5 03:08:53 EDT 2022
% 0.14/0.35  % 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.
% 0.14/0.39  % SZS status Theorem
% 0.14/0.39  % SZS output start Proof
% 0.14/0.39  tff(f_type, type, (
% 0.14/0.39     f: $i > $o)).
% 0.14/0.39  tff(tptp_fun_Y_0_type, type, (
% 0.14/0.39     tptp_fun_Y_0: $i)).
% 0.14/0.39  tff(g_type, type, (
% 0.14/0.39     g: $i > $o)).
% 0.14/0.39  tff(1,plain,
% 0.14/0.39      (^[Z: $i] : refl(((~f(Z)) | (~g(Z))) <=> ((~f(Z)) | (~g(Z))))),
% 0.14/0.39      inference(bind,[status(th)],[])).
% 0.14/0.39  tff(2,plain,
% 0.14/0.39      (![Z: $i] : ((~f(Z)) | (~g(Z))) <=> ![Z: $i] : ((~f(Z)) | (~g(Z)))),
% 0.14/0.39      inference(quant_intro,[status(thm)],[1])).
% 0.14/0.39  tff(3,plain,
% 0.14/0.39      (^[Z: $i] : trans(monotonicity(rewrite((f(Z) & g(Z)) <=> (~((~f(Z)) | (~g(Z))))), ((~(f(Z) & g(Z))) <=> (~(~((~f(Z)) | (~g(Z))))))), rewrite((~(~((~f(Z)) | (~g(Z))))) <=> ((~f(Z)) | (~g(Z)))), ((~(f(Z) & g(Z))) <=> ((~f(Z)) | (~g(Z)))))),
% 0.14/0.39      inference(bind,[status(th)],[])).
% 0.14/0.39  tff(4,plain,
% 0.14/0.39      (![Z: $i] : (~(f(Z) & g(Z))) <=> ![Z: $i] : ((~f(Z)) | (~g(Z)))),
% 0.14/0.39      inference(quant_intro,[status(thm)],[3])).
% 0.14/0.39  tff(5,plain,
% 0.14/0.39      ((~?[Z: $i] : (f(Z) & g(Z))) <=> (~?[Z: $i] : (f(Z) & g(Z)))),
% 0.14/0.39      inference(rewrite,[status(thm)],[])).
% 0.14/0.39  tff(6,plain,
% 0.14/0.39      ((~((![X: $i] : f(X) & ?[Y: $i] : g(Y)) => ?[Z: $i] : (f(Z) & g(Z)))) <=> (~((~(![X: $i] : f(X) & ?[Y: $i] : g(Y))) | ?[Z: $i] : (f(Z) & g(Z))))),
% 0.14/0.39      inference(rewrite,[status(thm)],[])).
% 0.14/0.39  tff(7,axiom,(~((![X: $i] : f(X) & ?[Y: $i] : g(Y)) => ?[Z: $i] : (f(Z) & g(Z)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','kalish239')).
% 0.14/0.39  tff(8,plain,
% 0.14/0.39      (~((~(![X: $i] : f(X) & ?[Y: $i] : g(Y))) | ?[Z: $i] : (f(Z) & g(Z)))),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[7, 6])).
% 0.14/0.39  tff(9,plain,
% 0.14/0.39      (~?[Z: $i] : (f(Z) & g(Z))),
% 0.14/0.39      inference(or_elim,[status(thm)],[8])).
% 0.14/0.39  tff(10,plain,
% 0.14/0.39      (~?[Z: $i] : (f(Z) & g(Z))),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[9, 5])).
% 0.14/0.39  tff(11,plain,
% 0.14/0.39      (~?[Z: $i] : (f(Z) & g(Z))),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[10, 5])).
% 0.14/0.39  tff(12,plain,
% 0.14/0.39      (~?[Z: $i] : (f(Z) & g(Z))),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[11, 5])).
% 0.14/0.39  tff(13,plain,
% 0.14/0.39      (~?[Z: $i] : (f(Z) & g(Z))),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[12, 5])).
% 0.14/0.39  tff(14,plain,
% 0.14/0.39      (~?[Z: $i] : (f(Z) & g(Z))),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[13, 5])).
% 0.14/0.39  tff(15,plain,
% 0.14/0.39      (~?[Z: $i] : (f(Z) & g(Z))),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[14, 5])).
% 0.14/0.39  tff(16,plain,
% 0.14/0.39      (^[Z: $i] : refl($oeq((~(f(Z) & g(Z))), (~(f(Z) & g(Z)))))),
% 0.14/0.39      inference(bind,[status(th)],[])).
% 0.14/0.39  tff(17,plain,(
% 0.14/0.39      ![Z: $i] : (~(f(Z) & g(Z)))),
% 0.14/0.39      inference(nnf-neg,[status(sab)],[15, 16])).
% 0.14/0.39  tff(18,plain,
% 0.14/0.39      (![Z: $i] : ((~f(Z)) | (~g(Z)))),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[17, 4])).
% 0.14/0.39  tff(19,plain,
% 0.14/0.39      (![Z: $i] : ((~f(Z)) | (~g(Z)))),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[18, 2])).
% 0.14/0.39  tff(20,plain,
% 0.14/0.39      (?[Y: $i] : g(Y) <=> ?[Y: $i] : g(Y)),
% 0.14/0.39      inference(rewrite,[status(thm)],[])).
% 0.14/0.39  tff(21,plain,
% 0.14/0.39      (![X: $i] : f(X) & ?[Y: $i] : g(Y)),
% 0.14/0.39      inference(or_elim,[status(thm)],[8])).
% 0.14/0.39  tff(22,plain,
% 0.14/0.39      (?[Y: $i] : g(Y)),
% 0.14/0.39      inference(and_elim,[status(thm)],[21])).
% 0.14/0.39  tff(23,plain,
% 0.14/0.39      (?[Y: $i] : g(Y)),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[22, 20])).
% 0.14/0.39  tff(24,plain,(
% 0.14/0.39      g(Y!0)),
% 0.14/0.39      inference(skolemize,[status(sab)],[23])).
% 0.14/0.39  tff(25,plain,
% 0.14/0.39      (((~![Z: $i] : ((~f(Z)) | (~g(Z)))) | ((~f(Y!0)) | (~g(Y!0)))) <=> ((~![Z: $i] : ((~f(Z)) | (~g(Z)))) | (~f(Y!0)) | (~g(Y!0)))),
% 0.14/0.39      inference(rewrite,[status(thm)],[])).
% 0.14/0.39  tff(26,plain,
% 0.14/0.39      ((~![Z: $i] : ((~f(Z)) | (~g(Z)))) | ((~f(Y!0)) | (~g(Y!0)))),
% 0.14/0.39      inference(quant_inst,[status(thm)],[])).
% 0.14/0.39  tff(27,plain,
% 0.14/0.39      ((~![Z: $i] : ((~f(Z)) | (~g(Z)))) | (~f(Y!0)) | (~g(Y!0))),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[26, 25])).
% 0.14/0.39  tff(28,plain,
% 0.14/0.39      (~f(Y!0)),
% 0.14/0.39      inference(unit_resolution,[status(thm)],[27, 24, 19])).
% 0.14/0.39  tff(29,plain,
% 0.14/0.39      (^[X: $i] : refl(f(X) <=> f(X))),
% 0.14/0.39      inference(bind,[status(th)],[])).
% 0.14/0.39  tff(30,plain,
% 0.14/0.39      (![X: $i] : f(X) <=> ![X: $i] : f(X)),
% 0.14/0.39      inference(quant_intro,[status(thm)],[29])).
% 0.14/0.39  tff(31,plain,
% 0.14/0.39      (![X: $i] : f(X) <=> ![X: $i] : f(X)),
% 0.14/0.39      inference(rewrite,[status(thm)],[])).
% 0.14/0.39  tff(32,plain,
% 0.14/0.39      (![X: $i] : f(X)),
% 0.14/0.39      inference(and_elim,[status(thm)],[21])).
% 0.14/0.39  tff(33,plain,
% 0.14/0.39      (![X: $i] : f(X)),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[32, 31])).
% 0.14/0.39  tff(34,plain,(
% 0.14/0.39      ![X: $i] : f(X)),
% 0.14/0.39      inference(skolemize,[status(sab)],[33])).
% 0.14/0.39  tff(35,plain,
% 0.14/0.39      (![X: $i] : f(X)),
% 0.14/0.39      inference(modus_ponens,[status(thm)],[34, 30])).
% 0.14/0.39  tff(36,plain,
% 0.14/0.39      ((~![X: $i] : f(X)) | f(Y!0)),
% 0.14/0.39      inference(quant_inst,[status(thm)],[])).
% 0.14/0.39  tff(37,plain,
% 0.14/0.39      ($false),
% 0.14/0.39      inference(unit_resolution,[status(thm)],[36, 35, 28])).
% 0.14/0.39  % SZS output end Proof
%------------------------------------------------------------------------------