TSTP Solution File: SYN399+1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYN399+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n019.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 23:55:10 EDT 2022

% Result   : Theorem 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN399+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n019.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 03:11:35 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.
% 0.20/0.39  % SZS status Theorem
% 0.20/0.39  % SZS output start Proof
% 0.20/0.39  tff(f_type, type, (
% 0.20/0.39     f: $i > $o)).
% 0.20/0.39  tff(tptp_fun_Y_0_type, type, (
% 0.20/0.39     tptp_fun_Y_0: $i)).
% 0.20/0.39  tff(p_type, type, (
% 0.20/0.39     p: $o)).
% 0.20/0.39  tff(1,assumption,(~f(Y!0)), introduced(assumption)).
% 0.20/0.39  tff(2,plain,
% 0.20/0.39      (^[X: $i] : refl((~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))) <=> (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))))),
% 0.20/0.39      inference(bind,[status(th)],[])).
% 0.20/0.39  tff(3,plain,
% 0.20/0.39      (![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))) <=> ![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))),
% 0.20/0.39      inference(quant_intro,[status(thm)],[2])).
% 0.20/0.39  tff(4,plain,
% 0.20/0.39      (^[X: $i] : rewrite((~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))) <=> (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))))),
% 0.20/0.39      inference(bind,[status(th)],[])).
% 0.20/0.39  tff(5,plain,
% 0.20/0.39      (![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))) <=> ![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))),
% 0.20/0.39      inference(quant_intro,[status(thm)],[4])).
% 0.20/0.39  tff(6,plain,
% 0.20/0.39      (![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y))))) <=> ![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))),
% 0.20/0.39      inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.39  tff(7,plain,
% 0.20/0.39      (^[X: $i] : trans(monotonicity(rewrite(((~f(X)) | (~f(Y!0))) <=> ((~f(X)) | (~f(Y!0)))), rewrite((f(X) | ![Y: $i] : f(Y)) <=> (f(X) | ![Y: $i] : f(Y))), ((((~f(X)) | (~f(Y!0))) & (f(X) | ![Y: $i] : f(Y))) <=> (((~f(X)) | (~f(Y!0))) & (f(X) | ![Y: $i] : f(Y))))), rewrite((((~f(X)) | (~f(Y!0))) & (f(X) | ![Y: $i] : f(Y))) <=> (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))), ((((~f(X)) | (~f(Y!0))) & (f(X) | ![Y: $i] : f(Y))) <=> (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))))),
% 0.20/0.39      inference(bind,[status(th)],[])).
% 0.20/0.39  tff(8,plain,
% 0.20/0.39      (![X: $i] : (((~f(X)) | (~f(Y!0))) & (f(X) | ![Y: $i] : f(Y))) <=> ![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))),
% 0.20/0.39      inference(quant_intro,[status(thm)],[7])).
% 0.20/0.39  tff(9,plain,
% 0.20/0.39      (^[X: $i] : rewrite((f(X) <=> p) <=> (f(X) <=> (~![Y: $i] : f(Y))))),
% 0.20/0.39      inference(bind,[status(th)],[])).
% 0.20/0.39  tff(10,plain,
% 0.20/0.39      (![X: $i] : (f(X) <=> p) <=> ![X: $i] : (f(X) <=> (~![Y: $i] : f(Y)))),
% 0.20/0.39      inference(quant_intro,[status(thm)],[9])).
% 0.20/0.39  tff(11,plain,
% 0.20/0.39      (![X: $i] : (f(X) <=> p) <=> ![X: $i] : (f(X) <=> p)),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(12,plain,
% 0.20/0.39      ((~(![X: $i] : (f(X) <=> p) => (![Y: $i] : f(Y) <=> p))) <=> (~((~![X: $i] : (f(X) <=> p)) | (![Y: $i] : f(Y) <=> p)))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(13,axiom,(~(![X: $i] : (f(X) <=> p) => (![Y: $i] : f(Y) <=> p))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','kalish223')).
% 0.20/0.39  tff(14,plain,
% 0.20/0.39      (~((~![X: $i] : (f(X) <=> p)) | (![Y: $i] : f(Y) <=> p))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.39  tff(15,plain,
% 0.20/0.39      (![X: $i] : (f(X) <=> p)),
% 0.20/0.39      inference(or_elim,[status(thm)],[14])).
% 0.20/0.39  tff(16,plain,
% 0.20/0.39      (![X: $i] : (f(X) <=> p)),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.39  tff(17,plain,
% 0.20/0.39      (![X: $i] : (f(X) <=> (~![Y: $i] : f(Y)))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[16, 10])).
% 0.20/0.39  tff(18,plain,(
% 0.20/0.39      ![X: $i] : (((~f(X)) | (~f(Y!0))) & (f(X) | ![Y: $i] : f(Y)))),
% 0.20/0.39      inference(skolemize,[status(sab)],[17])).
% 0.20/0.39  tff(19,plain,
% 0.20/0.39      (![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[18, 8])).
% 0.20/0.39  tff(20,plain,
% 0.20/0.39      (![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[19, 6])).
% 0.20/0.39  tff(21,plain,
% 0.20/0.39      (((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y)))))) <=> ((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y))))))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(22,plain,
% 0.20/0.39      ((~((~((~f(Y!0)) | (~f(Y!0)))) | (~(f(Y!0) | ![Y: $i] : f(Y))))) <=> (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y)))))),
% 0.20/0.39      inference(rewrite,[status(thm)],[])).
% 0.20/0.39  tff(23,plain,
% 0.20/0.39      (((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~((~((~f(Y!0)) | (~f(Y!0)))) | (~(f(Y!0) | ![Y: $i] : f(Y)))))) <=> ((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y))))))),
% 0.20/0.39      inference(monotonicity,[status(thm)],[22])).
% 0.20/0.39  tff(24,plain,
% 0.20/0.39      (((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~((~((~f(Y!0)) | (~f(Y!0)))) | (~(f(Y!0) | ![Y: $i] : f(Y)))))) <=> ((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y))))))),
% 0.20/0.39      inference(transitivity,[status(thm)],[23, 21])).
% 0.20/0.39  tff(25,plain,
% 0.20/0.39      ((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~((~((~f(Y!0)) | (~f(Y!0)))) | (~(f(Y!0) | ![Y: $i] : f(Y)))))),
% 0.20/0.39      inference(quant_inst,[status(thm)],[])).
% 0.20/0.39  tff(26,plain,
% 0.20/0.39      ((~![X: $i] : (~((~((~f(X)) | (~f(Y!0)))) | (~(f(X) | ![Y: $i] : f(Y)))))) | (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y)))))),
% 0.20/0.39      inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.39  tff(27,plain,
% 0.20/0.39      (~(f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y))))),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[26, 20])).
% 0.20/0.39  tff(28,plain,
% 0.20/0.39      ((f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y)))) | (f(Y!0) | ![Y: $i] : f(Y))),
% 0.20/0.39      inference(tautology,[status(thm)],[])).
% 0.20/0.39  tff(29,plain,
% 0.20/0.39      (f(Y!0) | ![Y: $i] : f(Y)),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[28, 27])).
% 0.20/0.39  tff(30,plain,
% 0.20/0.39      ((~(f(Y!0) | ![Y: $i] : f(Y))) | f(Y!0) | ![Y: $i] : f(Y)),
% 0.20/0.39      inference(tautology,[status(thm)],[])).
% 0.20/0.39  tff(31,plain,
% 0.20/0.39      ((~(f(Y!0) | ![Y: $i] : f(Y))) | ![Y: $i] : f(Y)),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[30, 1])).
% 0.20/0.39  tff(32,plain,
% 0.20/0.39      (![Y: $i] : f(Y)),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[31, 29])).
% 0.20/0.39  tff(33,plain,
% 0.20/0.39      ((~![Y: $i] : f(Y)) | f(Y!0)),
% 0.20/0.39      inference(quant_inst,[status(thm)],[])).
% 0.20/0.39  tff(34,plain,
% 0.20/0.39      ($false),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[33, 32, 1])).
% 0.20/0.39  tff(35,plain,(f(Y!0)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39  tff(36,plain,
% 0.20/0.39      ((f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y)))) | (~f(Y!0))),
% 0.20/0.39      inference(tautology,[status(thm)],[])).
% 0.20/0.39  tff(37,plain,
% 0.20/0.39      (f(Y!0) | (~(f(Y!0) | ![Y: $i] : f(Y)))),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.39  tff(38,plain,
% 0.20/0.39      ($false),
% 0.20/0.39      inference(unit_resolution,[status(thm)],[26, 20, 37])).
% 0.20/0.39  % SZS output end Proof
%------------------------------------------------------------------------------