TSTP Solution File: SYN049+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN049+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n008.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 23:53:20 EDT 2022

% Result   : Theorem 0.13s 0.38s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SYN049+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n008.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 01:24:10 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.
% 0.13/0.38  % SZS status Theorem
% 0.13/0.38  % SZS output start Proof
% 0.13/0.38  tff(big_p_type, type, (
% 0.13/0.38     big_p: $i > $o)).
% 0.13/0.38  tff(tptp_fun_Y_1_type, type, (
% 0.13/0.38     tptp_fun_Y_1: $i > $i)).
% 0.13/0.38  tff(tptp_fun_Z_0_type, type, (
% 0.13/0.38     tptp_fun_Z_0: $i > $i)).
% 0.13/0.38  tff(elem_2_type, type, (
% 0.13/0.38     elem_2: $i)).
% 0.13/0.38  tff(big_q_type, type, (
% 0.13/0.38     big_q: $i > $o)).
% 0.13/0.38  tff(1,assumption,(big_q(tptp_fun_Y_1(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Y_1(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Y_1(elem!2))))))), introduced(assumption)).
% 0.13/0.38  tff(2,plain,
% 0.13/0.38      (^[X: $i] : refl((~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X))))))) <=> (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X))))))))),
% 0.13/0.38      inference(bind,[status(th)],[])).
% 0.13/0.38  tff(3,plain,
% 0.13/0.38      (![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X))))))) <=> ![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))),
% 0.13/0.38      inference(quant_intro,[status(thm)],[2])).
% 0.13/0.38  tff(4,plain,
% 0.13/0.38      ((~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y))))))),
% 0.13/0.38      inference(rewrite,[status(thm)],[])).
% 0.13/0.38  tff(5,plain,
% 0.13/0.38      ((~?[X: $i] : ![Y: $i, Z: $i] : ((big_p(Y) => big_q(Z)) => (big_p(X) => big_q(X)))) <=> (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y))))))),
% 0.13/0.38      inference(rewrite,[status(thm)],[])).
% 0.13/0.38  tff(6,axiom,(~?[X: $i] : ![Y: $i, Z: $i] : ((big_p(Y) => big_q(Z)) => (big_p(X) => big_q(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pel19')).
% 0.13/0.38  tff(7,plain,
% 0.13/0.38      (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.38  tff(8,plain,
% 0.13/0.38      (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[7, 4])).
% 0.13/0.38  tff(9,plain,
% 0.13/0.38      (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.38  tff(10,plain,
% 0.13/0.38      (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[9, 4])).
% 0.13/0.38  tff(11,plain,
% 0.13/0.38      (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[10, 4])).
% 0.13/0.38  tff(12,plain,
% 0.13/0.38      (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[11, 4])).
% 0.13/0.38  tff(13,plain,
% 0.13/0.38      (~?[X: $i] : ![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[12, 4])).
% 0.13/0.38  tff(14,plain,
% 0.13/0.38      (^[X: $i] : sk($oeq((~![Y: $i, Z: $i] : (big_q(X) | (~big_p(X)) | (~(big_q(Z) | (~big_p(Y)))))), (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))))),
% 0.13/0.38      inference(bind,[status(th)],[])).
% 0.13/0.38  tff(15,plain,(
% 0.13/0.38      ![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))),
% 0.13/0.38      inference(nnf-neg,[status(sab)],[13, 14])).
% 0.13/0.38  tff(16,plain,
% 0.13/0.38      (![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[15, 3])).
% 0.13/0.38  tff(17,plain,
% 0.13/0.38      ((~![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))) | (~(big_q(tptp_fun_Y_1(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Y_1(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Y_1(elem!2))))))))),
% 0.13/0.38      inference(quant_inst,[status(thm)],[])).
% 0.13/0.38  tff(18,plain,
% 0.13/0.38      ($false),
% 0.13/0.38      inference(unit_resolution,[status(thm)],[17, 16, 1])).
% 0.13/0.38  tff(19,plain,(~(big_q(tptp_fun_Y_1(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Y_1(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Y_1(elem!2)))))))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.38  tff(20,plain,
% 0.13/0.38      ((big_q(tptp_fun_Y_1(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Y_1(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Y_1(elem!2))))))) | big_p(tptp_fun_Y_1(elem!2))),
% 0.13/0.39      inference(tautology,[status(thm)],[])).
% 0.13/0.39  tff(21,plain,
% 0.13/0.39      (big_p(tptp_fun_Y_1(elem!2))),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[20, 19])).
% 0.13/0.39  tff(22,plain,
% 0.13/0.39      ((~![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))) | (~(big_q(elem!2) | (~big_p(elem!2)) | (~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))))))),
% 0.13/0.39      inference(quant_inst,[status(thm)],[])).
% 0.13/0.39  tff(23,plain,
% 0.13/0.39      (~(big_q(elem!2) | (~big_p(elem!2)) | (~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))))))),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[22, 16])).
% 0.13/0.39  tff(24,plain,
% 0.13/0.39      ((big_q(elem!2) | (~big_p(elem!2)) | (~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))))) | (big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))))),
% 0.13/0.39      inference(tautology,[status(thm)],[])).
% 0.13/0.39  tff(25,plain,
% 0.13/0.39      (big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[24, 23])).
% 0.13/0.39  tff(26,plain,
% 0.13/0.39      ((~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2))))) | big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))),
% 0.13/0.39      inference(tautology,[status(thm)],[])).
% 0.13/0.39  tff(27,plain,
% 0.13/0.39      (big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Y_1(elem!2)))),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[26, 25])).
% 0.13/0.39  tff(28,plain,
% 0.13/0.39      (big_q(tptp_fun_Z_0(elem!2))),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[27, 21])).
% 0.13/0.39  tff(29,plain,
% 0.13/0.39      ((big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Z_0(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))) | (~big_q(tptp_fun_Z_0(elem!2)))),
% 0.13/0.39      inference(tautology,[status(thm)],[])).
% 0.13/0.39  tff(30,plain,
% 0.13/0.39      (big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Z_0(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.39  tff(31,plain,
% 0.13/0.39      ((~![X: $i] : (~(big_q(X) | (~big_p(X)) | (~(big_q(tptp_fun_Z_0(X)) | (~big_p(tptp_fun_Y_1(X)))))))) | (~(big_q(tptp_fun_Z_0(elem!2)) | (~big_p(tptp_fun_Z_0(elem!2))) | (~(big_q(tptp_fun_Z_0(tptp_fun_Z_0(elem!2))) | (~big_p(tptp_fun_Y_1(tptp_fun_Z_0(elem!2))))))))),
% 0.13/0.39      inference(quant_inst,[status(thm)],[])).
% 0.13/0.39  tff(32,plain,
% 0.13/0.39      ($false),
% 0.13/0.39      inference(unit_resolution,[status(thm)],[31, 16, 30])).
% 0.13/0.39  % SZS output end Proof
%------------------------------------------------------------------------------