TSTP Solution File: SYN362+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN362+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n022.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 23:54:59 EDT 2022

% Result   : Theorem 0.13s 0.37s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN362+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n022.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 02:56:09 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.
% 0.13/0.37  % SZS status Theorem
% 0.13/0.37  % SZS output start Proof
% 0.13/0.37  tff(big_p_type, type, (
% 0.13/0.37     big_p: $i > $o)).
% 0.13/0.37  tff(tptp_fun_W_0_type, type, (
% 0.13/0.37     tptp_fun_W_0: $i > $i)).
% 0.13/0.37  tff(tptp_fun_Z_1_type, type, (
% 0.13/0.37     tptp_fun_Z_1: $i)).
% 0.13/0.37  tff(big_r_type, type, (
% 0.13/0.37     big_r: ( $i * $i ) > $o)).
% 0.13/0.37  tff(1,plain,
% 0.13/0.37      (![Y: $i] : ?[W: $i] : big_r(Y, W) <=> ![Y: $i] : ?[W: $i] : big_r(Y, W)),
% 0.13/0.37      inference(rewrite,[status(thm)],[])).
% 0.13/0.37  tff(2,plain,
% 0.13/0.37      ((~((![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : (big_p(X) => (~big_r(Z, X)))) => ?[X: $i] : (~big_p(X)))) <=> (~((~(![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X))))) | ?[X: $i] : (~big_p(X))))),
% 0.13/0.37      inference(rewrite,[status(thm)],[])).
% 0.13/0.37  tff(3,axiom,(~((![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : (big_p(X) => (~big_r(Z, X)))) => ?[X: $i] : (~big_p(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','x2113')).
% 0.13/0.37  tff(4,plain,
% 0.13/0.37      (~((~(![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X))))) | ?[X: $i] : (~big_p(X)))),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.37  tff(5,plain,
% 0.13/0.37      (![Y: $i] : ?[W: $i] : big_r(Y, W) & ?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X)))),
% 0.13/0.37      inference(or_elim,[status(thm)],[4])).
% 0.13/0.37  tff(6,plain,
% 0.13/0.37      (![Y: $i] : ?[W: $i] : big_r(Y, W)),
% 0.13/0.37      inference(and_elim,[status(thm)],[5])).
% 0.13/0.37  tff(7,plain,
% 0.13/0.37      (![Y: $i] : ?[W: $i] : big_r(Y, W)),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.37  tff(8,plain,(
% 0.13/0.37      ![Y: $i] : big_r(Y, tptp_fun_W_0(Y))),
% 0.13/0.37      inference(skolemize,[status(sab)],[7])).
% 0.13/0.37  tff(9,plain,
% 0.13/0.37      ((~![Y: $i] : big_r(Y, tptp_fun_W_0(Y))) | big_r(Z!1, tptp_fun_W_0(Z!1))),
% 0.13/0.37      inference(quant_inst,[status(thm)],[])).
% 0.13/0.37  tff(10,plain,
% 0.13/0.37      (big_r(Z!1, tptp_fun_W_0(Z!1))),
% 0.13/0.37      inference(unit_resolution,[status(thm)],[9, 8])).
% 0.13/0.37  tff(11,plain,
% 0.13/0.37      (^[X: $i] : refl(((~big_p(X)) | (~big_r(Z!1, X))) <=> ((~big_p(X)) | (~big_r(Z!1, X))))),
% 0.13/0.37      inference(bind,[status(th)],[])).
% 0.13/0.37  tff(12,plain,
% 0.13/0.37      (![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X))) <=> ![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))),
% 0.13/0.37      inference(quant_intro,[status(thm)],[11])).
% 0.13/0.37  tff(13,plain,
% 0.13/0.37      (?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X))) <=> ?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X)))),
% 0.13/0.37      inference(rewrite,[status(thm)],[])).
% 0.13/0.37  tff(14,plain,
% 0.13/0.37      (?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X)))),
% 0.13/0.37      inference(and_elim,[status(thm)],[5])).
% 0.13/0.37  tff(15,plain,
% 0.13/0.37      (?[Z: $i] : ![X: $i] : ((~big_p(X)) | (~big_r(Z, X)))),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[14, 13])).
% 0.13/0.37  tff(16,plain,(
% 0.13/0.37      $oeq(![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X))), ![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X))))),
% 0.13/0.37      inference(transitivity,[status(sab)],[15])).
% 0.13/0.37  tff(17,plain,
% 0.13/0.37      (![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[16, 12])).
% 0.13/0.37  tff(18,plain,
% 0.13/0.37      (((~![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))) | ((~big_p(tptp_fun_W_0(Z!1))) | (~big_r(Z!1, tptp_fun_W_0(Z!1))))) <=> ((~![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))) | (~big_p(tptp_fun_W_0(Z!1))) | (~big_r(Z!1, tptp_fun_W_0(Z!1))))),
% 0.13/0.37      inference(rewrite,[status(thm)],[])).
% 0.13/0.37  tff(19,plain,
% 0.13/0.37      ((~![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))) | ((~big_p(tptp_fun_W_0(Z!1))) | (~big_r(Z!1, tptp_fun_W_0(Z!1))))),
% 0.13/0.37      inference(quant_inst,[status(thm)],[])).
% 0.13/0.37  tff(20,plain,
% 0.13/0.37      ((~![X: $i] : ((~big_p(X)) | (~big_r(Z!1, X)))) | (~big_p(tptp_fun_W_0(Z!1))) | (~big_r(Z!1, tptp_fun_W_0(Z!1)))),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[19, 18])).
% 0.13/0.37  tff(21,plain,
% 0.13/0.37      (~big_p(tptp_fun_W_0(Z!1))),
% 0.13/0.37      inference(unit_resolution,[status(thm)],[20, 17, 10])).
% 0.13/0.37  tff(22,plain,
% 0.13/0.37      (^[X: $i] : refl(big_p(X) <=> big_p(X))),
% 0.13/0.37      inference(bind,[status(th)],[])).
% 0.13/0.37  tff(23,plain,
% 0.13/0.37      (![X: $i] : big_p(X) <=> ![X: $i] : big_p(X)),
% 0.13/0.37      inference(quant_intro,[status(thm)],[22])).
% 0.13/0.37  tff(24,plain,
% 0.13/0.37      (^[X: $i] : rewrite((~(~big_p(X))) <=> big_p(X))),
% 0.13/0.37      inference(bind,[status(th)],[])).
% 0.13/0.37  tff(25,plain,
% 0.13/0.37      (![X: $i] : (~(~big_p(X))) <=> ![X: $i] : big_p(X)),
% 0.13/0.37      inference(quant_intro,[status(thm)],[24])).
% 0.13/0.37  tff(26,plain,
% 0.13/0.37      ((~?[X: $i] : (~big_p(X))) <=> (~?[X: $i] : (~big_p(X)))),
% 0.13/0.37      inference(rewrite,[status(thm)],[])).
% 0.13/0.37  tff(27,plain,
% 0.13/0.37      (~?[X: $i] : (~big_p(X))),
% 0.13/0.37      inference(or_elim,[status(thm)],[4])).
% 0.13/0.37  tff(28,plain,
% 0.13/0.37      (~?[X: $i] : (~big_p(X))),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.37  tff(29,plain,
% 0.13/0.37      (~?[X: $i] : (~big_p(X))),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[28, 26])).
% 0.13/0.37  tff(30,plain,
% 0.13/0.37      (~?[X: $i] : (~big_p(X))),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[29, 26])).
% 0.13/0.37  tff(31,plain,
% 0.13/0.37      (~?[X: $i] : (~big_p(X))),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[30, 26])).
% 0.13/0.37  tff(32,plain,
% 0.13/0.37      (~?[X: $i] : (~big_p(X))),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[31, 26])).
% 0.13/0.37  tff(33,plain,
% 0.13/0.37      (~?[X: $i] : (~big_p(X))),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[32, 26])).
% 0.13/0.37  tff(34,plain,
% 0.13/0.37      (^[X: $i] : refl($oeq((~(~big_p(X))), (~(~big_p(X)))))),
% 0.13/0.37      inference(bind,[status(th)],[])).
% 0.13/0.37  tff(35,plain,(
% 0.13/0.37      ![X: $i] : (~(~big_p(X)))),
% 0.13/0.37      inference(nnf-neg,[status(sab)],[33, 34])).
% 0.13/0.37  tff(36,plain,
% 0.13/0.37      (![X: $i] : big_p(X)),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[35, 25])).
% 0.13/0.37  tff(37,plain,
% 0.13/0.37      (![X: $i] : big_p(X)),
% 0.13/0.37      inference(modus_ponens,[status(thm)],[36, 23])).
% 0.13/0.37  tff(38,plain,
% 0.13/0.37      ((~![X: $i] : big_p(X)) | big_p(tptp_fun_W_0(Z!1))),
% 0.13/0.37      inference(quant_inst,[status(thm)],[])).
% 0.13/0.37  tff(39,plain,
% 0.13/0.37      ($false),
% 0.13/0.37      inference(unit_resolution,[status(thm)],[38, 37, 21])).
% 0.13/0.37  % SZS output end Proof
%------------------------------------------------------------------------------