TSTP Solution File: SET019+4 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SET019+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n028.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 : Tue Sep 20 05:04:52 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
% 0.11/0.12  % Problem  : SET019+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Sat Sep  3 01:23:53 EDT 2022
% 0.13/0.33  % 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(subset_type, type, (
% 0.13/0.38     subset: ( $i * $i ) > $o)).
% 0.13/0.38  tff(tptp_fun_A_4_type, type, (
% 0.13/0.38     tptp_fun_A_4: $i)).
% 0.13/0.38  tff(tptp_fun_B_3_type, type, (
% 0.13/0.38     tptp_fun_B_3: $i)).
% 0.13/0.38  tff(equal_set_type, type, (
% 0.13/0.38     equal_set: ( $i * $i ) > $o)).
% 0.13/0.38  tff(1,plain,
% 0.13/0.38      ((~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))) <=> (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B)))),
% 0.13/0.38      inference(rewrite,[status(thm)],[])).
% 0.13/0.38  tff(2,plain,
% 0.13/0.38      ((~![A: $i, B: $i] : ((subset(A, B) & subset(B, A)) => equal_set(A, B))) <=> (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B)))),
% 0.13/0.38      inference(rewrite,[status(thm)],[])).
% 0.13/0.38  tff(3,axiom,(~![A: $i, B: $i] : ((subset(A, B) & subset(B, A)) => equal_set(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thI02')).
% 0.13/0.38  tff(4,plain,
% 0.13/0.38      (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[3, 2])).
% 0.13/0.38  tff(5,plain,
% 0.13/0.38      (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[4, 1])).
% 0.13/0.38  tff(6,plain,
% 0.13/0.38      (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[5, 1])).
% 0.13/0.38  tff(7,plain,
% 0.13/0.38      (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[6, 1])).
% 0.13/0.38  tff(8,plain,
% 0.13/0.38      (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[7, 1])).
% 0.13/0.38  tff(9,plain,
% 0.13/0.38      (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[8, 1])).
% 0.13/0.38  tff(10,plain,
% 0.13/0.38      (~![A: $i, B: $i] : ((~(subset(A, B) & subset(B, A))) | equal_set(A, B))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[9, 1])).
% 0.13/0.38  tff(11,plain,(
% 0.13/0.38      ~((~(subset(A!4, B!3) & subset(B!3, A!4))) | equal_set(A!4, B!3))),
% 0.13/0.38      inference(skolemize,[status(sab)],[10])).
% 0.13/0.38  tff(12,plain,
% 0.13/0.38      (subset(A!4, B!3) & subset(B!3, A!4)),
% 0.13/0.38      inference(or_elim,[status(thm)],[11])).
% 0.13/0.38  tff(13,plain,
% 0.13/0.38      (subset(B!3, A!4)),
% 0.13/0.38      inference(and_elim,[status(thm)],[12])).
% 0.13/0.38  tff(14,plain,
% 0.13/0.38      (subset(A!4, B!3)),
% 0.13/0.38      inference(and_elim,[status(thm)],[12])).
% 0.13/0.38  tff(15,plain,
% 0.13/0.38      ((~((~subset(A!4, B!3)) | (~subset(B!3, A!4)))) | (~subset(A!4, B!3)) | (~subset(B!3, A!4))),
% 0.13/0.38      inference(tautology,[status(thm)],[])).
% 0.13/0.38  tff(16,plain,
% 0.13/0.38      (~((~subset(A!4, B!3)) | (~subset(B!3, A!4)))),
% 0.13/0.38      inference(unit_resolution,[status(thm)],[15, 14, 13])).
% 0.13/0.38  tff(17,plain,
% 0.13/0.38      (~equal_set(A!4, B!3)),
% 0.13/0.38      inference(or_elim,[status(thm)],[11])).
% 0.13/0.38  tff(18,plain,
% 0.13/0.38      ((~(equal_set(A!4, B!3) <=> (~((~subset(A!4, B!3)) | (~subset(B!3, A!4)))))) | equal_set(A!4, B!3) | ((~subset(A!4, B!3)) | (~subset(B!3, A!4)))),
% 0.13/0.38      inference(tautology,[status(thm)],[])).
% 0.13/0.38  tff(19,plain,
% 0.13/0.38      (~(equal_set(A!4, B!3) <=> (~((~subset(A!4, B!3)) | (~subset(B!3, A!4)))))),
% 0.13/0.38      inference(unit_resolution,[status(thm)],[18, 17, 16])).
% 0.13/0.38  tff(20,plain,
% 0.13/0.38      (^[A: $i, B: $i] : refl((equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.13/0.38      inference(bind,[status(th)],[])).
% 0.13/0.38  tff(21,plain,
% 0.13/0.38      (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.38      inference(quant_intro,[status(thm)],[20])).
% 0.13/0.38  tff(22,plain,
% 0.13/0.38      (^[A: $i, B: $i] : rewrite((equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.13/0.38      inference(bind,[status(th)],[])).
% 0.13/0.38  tff(23,plain,
% 0.13/0.38      (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.38      inference(quant_intro,[status(thm)],[22])).
% 0.13/0.38  tff(24,plain,
% 0.13/0.38      (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.38      inference(rewrite,[status(thm)],[])).
% 0.13/0.38  tff(25,axiom,(![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax','equal_set')).
% 0.13/0.38  tff(26,plain,
% 0.13/0.38      (![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[25, 24])).
% 0.13/0.38  tff(27,plain,(
% 0.13/0.38      ![A: $i, B: $i] : (equal_set(A, B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.38      inference(skolemize,[status(sab)],[26])).
% 0.13/0.38  tff(28,plain,
% 0.13/0.38      (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[27, 23])).
% 0.13/0.38  tff(29,plain,
% 0.13/0.38      (![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.38      inference(modus_ponens,[status(thm)],[28, 21])).
% 0.13/0.38  tff(30,plain,
% 0.13/0.38      ((~![A: $i, B: $i] : (equal_set(A, B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | (equal_set(A!4, B!3) <=> (~((~subset(A!4, B!3)) | (~subset(B!3, A!4)))))),
% 0.13/0.38      inference(quant_inst,[status(thm)],[])).
% 0.13/0.38  tff(31,plain,
% 0.13/0.38      ($false),
% 0.13/0.38      inference(unit_resolution,[status(thm)],[30, 29, 19])).
% 0.13/0.38  % SZS output end Proof
%------------------------------------------------------------------------------