TSTP Solution File: SEU123+2 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SEU123+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n007.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 07:27:35 EDT 2022

% Result   : Theorem 0.13s 0.40s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SEU123+2 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n007.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Sep  3 09:18:04 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.13/0.40  % SZS status Theorem
% 0.13/0.40  % SZS output start Proof
% 0.13/0.40  tff(subset_type, type, (
% 0.13/0.40     subset: ( $i * $i ) > $o)).
% 0.13/0.40  tff(tptp_fun_A_6_type, type, (
% 0.13/0.40     tptp_fun_A_6: $i)).
% 0.13/0.40  tff(empty_set_type, type, (
% 0.13/0.40     empty_set: $i)).
% 0.13/0.40  tff(1,plain,
% 0.13/0.40      (^[A: $i, B: $i] : refl(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.13/0.40      inference(bind,[status(th)],[])).
% 0.13/0.40  tff(2,plain,
% 0.13/0.40      (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.40      inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40  tff(3,plain,
% 0.13/0.40      (^[A: $i, B: $i] : rewrite(((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.13/0.40      inference(bind,[status(th)],[])).
% 0.13/0.40  tff(4,plain,
% 0.13/0.40      (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.40      inference(quant_intro,[status(thm)],[3])).
% 0.13/0.40  tff(5,plain,
% 0.13/0.40      (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.40      inference(rewrite,[status(thm)],[])).
% 0.13/0.40  tff(6,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.13/0.40  tff(7,plain,
% 0.13/0.40      (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.40  tff(8,plain,(
% 0.13/0.40      ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.13/0.40      inference(skolemize,[status(sab)],[7])).
% 0.13/0.40  tff(9,plain,
% 0.13/0.40      (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.40  tff(10,plain,
% 0.13/0.40      (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.40  tff(11,plain,
% 0.13/0.40      ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((A!6 = empty_set) <=> (~((~subset(A!6, empty_set)) | (~subset(empty_set, A!6)))))),
% 0.13/0.40      inference(quant_inst,[status(thm)],[])).
% 0.13/0.40  tff(12,plain,
% 0.13/0.40      ((A!6 = empty_set) <=> (~((~subset(A!6, empty_set)) | (~subset(empty_set, A!6))))),
% 0.13/0.40      inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.40  tff(13,plain,
% 0.13/0.40      ((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) <=> (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set)))),
% 0.13/0.40      inference(rewrite,[status(thm)],[])).
% 0.13/0.40  tff(14,plain,
% 0.13/0.40      ((~![A: $i] : (subset(A, empty_set) => (A = empty_set))) <=> (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set)))),
% 0.13/0.40      inference(rewrite,[status(thm)],[])).
% 0.13/0.40  tff(15,axiom,(~![A: $i] : (subset(A, empty_set) => (A = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_xboole_1')).
% 0.13/0.40  tff(16,plain,
% 0.13/0.40      (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.40  tff(17,plain,
% 0.13/0.40      (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[16, 13])).
% 0.13/0.40  tff(18,plain,
% 0.13/0.40      (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.40  tff(19,plain,
% 0.13/0.40      (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[18, 13])).
% 0.13/0.40  tff(20,plain,
% 0.13/0.40      (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[19, 13])).
% 0.13/0.40  tff(21,plain,
% 0.13/0.40      (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.40  tff(22,plain,
% 0.13/0.40      (~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[21, 13])).
% 0.13/0.40  tff(23,plain,(
% 0.13/0.40      ~((~subset(A!6, empty_set)) | (A!6 = empty_set))),
% 0.13/0.40      inference(skolemize,[status(sab)],[22])).
% 0.13/0.40  tff(24,plain,
% 0.13/0.40      (~(A!6 = empty_set)),
% 0.13/0.40      inference(or_elim,[status(thm)],[23])).
% 0.13/0.40  tff(25,plain,
% 0.13/0.40      ((~((A!6 = empty_set) <=> (~((~subset(A!6, empty_set)) | (~subset(empty_set, A!6)))))) | (A!6 = empty_set) | ((~subset(A!6, empty_set)) | (~subset(empty_set, A!6)))),
% 0.13/0.40      inference(tautology,[status(thm)],[])).
% 0.13/0.41  tff(26,plain,
% 0.13/0.41      ((~((A!6 = empty_set) <=> (~((~subset(A!6, empty_set)) | (~subset(empty_set, A!6)))))) | ((~subset(A!6, empty_set)) | (~subset(empty_set, A!6)))),
% 0.13/0.41      inference(unit_resolution,[status(thm)],[25, 24])).
% 0.13/0.41  tff(27,plain,
% 0.13/0.41      ((~subset(A!6, empty_set)) | (~subset(empty_set, A!6))),
% 0.13/0.41      inference(unit_resolution,[status(thm)],[26, 12])).
% 0.13/0.41  tff(28,plain,
% 0.13/0.41      (subset(A!6, empty_set)),
% 0.13/0.41      inference(or_elim,[status(thm)],[23])).
% 0.13/0.41  tff(29,plain,
% 0.13/0.41      ((~((~subset(A!6, empty_set)) | (~subset(empty_set, A!6)))) | (~subset(A!6, empty_set)) | (~subset(empty_set, A!6))),
% 0.13/0.41      inference(tautology,[status(thm)],[])).
% 0.13/0.41  tff(30,plain,
% 0.13/0.41      ((~((~subset(A!6, empty_set)) | (~subset(empty_set, A!6)))) | (~subset(empty_set, A!6))),
% 0.13/0.41      inference(unit_resolution,[status(thm)],[29, 28])).
% 0.13/0.41  tff(31,plain,
% 0.13/0.41      (~subset(empty_set, A!6)),
% 0.13/0.41      inference(unit_resolution,[status(thm)],[30, 27])).
% 0.13/0.41  tff(32,plain,
% 0.13/0.41      (^[A: $i] : refl(subset(empty_set, A) <=> subset(empty_set, A))),
% 0.13/0.41      inference(bind,[status(th)],[])).
% 0.13/0.41  tff(33,plain,
% 0.13/0.41      (![A: $i] : subset(empty_set, A) <=> ![A: $i] : subset(empty_set, A)),
% 0.13/0.41      inference(quant_intro,[status(thm)],[32])).
% 0.13/0.41  tff(34,plain,
% 0.13/0.41      (![A: $i] : subset(empty_set, A) <=> ![A: $i] : subset(empty_set, A)),
% 0.13/0.41      inference(rewrite,[status(thm)],[])).
% 0.13/0.41  tff(35,axiom,(![A: $i] : subset(empty_set, A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_xboole_1')).
% 0.13/0.41  tff(36,plain,
% 0.13/0.41      (![A: $i] : subset(empty_set, A)),
% 0.13/0.41      inference(modus_ponens,[status(thm)],[35, 34])).
% 0.13/0.41  tff(37,plain,(
% 0.13/0.41      ![A: $i] : subset(empty_set, A)),
% 0.13/0.41      inference(skolemize,[status(sab)],[36])).
% 0.13/0.41  tff(38,plain,
% 0.13/0.41      (![A: $i] : subset(empty_set, A)),
% 0.13/0.41      inference(modus_ponens,[status(thm)],[37, 33])).
% 0.13/0.41  tff(39,plain,
% 0.13/0.41      ((~![A: $i] : subset(empty_set, A)) | subset(empty_set, A!6)),
% 0.13/0.41      inference(quant_inst,[status(thm)],[])).
% 0.13/0.41  tff(40,plain,
% 0.13/0.41      ($false),
% 0.13/0.41      inference(unit_resolution,[status(thm)],[39, 38, 31])).
% 0.13/0.41  % SZS output end Proof
%------------------------------------------------------------------------------