TSTP Solution File: DAT081_1 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : DAT081_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n025.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 : Fri Sep 16 14:36:39 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
% 0.07/0.12  % Problem  : DAT081_1 : TPTP v8.1.0. Released v6.1.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n025.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 : Wed Aug 31 01:57:45 EDT 2022
% 0.13/0.34  % 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(count_type, type, (
% 0.13/0.40     count: ( $int * list ) > $int)).
% 0.13/0.40  tff(nil_type, type, (
% 0.13/0.40     nil: list)).
% 0.13/0.40  tff(tptp_fun_A_6_type, type, (
% 0.13/0.40     tptp_fun_A_6: $int)).
% 0.13/0.40  tff(in_type, type, (
% 0.13/0.40     in: ( $int * list ) > $o)).
% 0.13/0.40  tff(1,plain,
% 0.13/0.40      (^[N: $int, L: list] : refl((in(N, L) <=> (~$lesseq(count(N, L), 0))) <=> (in(N, L) <=> (~$lesseq(count(N, L), 0))))),
% 0.13/0.40      inference(bind,[status(th)],[])).
% 0.13/0.40  tff(2,plain,
% 0.13/0.40      (![N: $int, L: list] : (in(N, L) <=> (~$lesseq(count(N, L), 0))) <=> ![N: $int, L: list] : (in(N, L) <=> (~$lesseq(count(N, L), 0)))),
% 0.13/0.40      inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40  tff(3,plain,
% 0.13/0.40      (![N: $int, L: list] : (in(N, L) <=> (~$lesseq(count(N, L), 0))) <=> ![N: $int, L: list] : (in(N, L) <=> (~$lesseq(count(N, L), 0)))),
% 0.13/0.40      inference(rewrite,[status(thm)],[])).
% 0.13/0.40  tff(4,plain,
% 0.13/0.40      (^[N: $int, L: list] : rewrite((in(N, L) <=> $greater(count(N, L), 0)) <=> (in(N, L) <=> (~$lesseq(count(N, L), 0))))),
% 0.13/0.40      inference(bind,[status(th)],[])).
% 0.13/0.40  tff(5,plain,
% 0.13/0.40      (![N: $int, L: list] : (in(N, L) <=> $greater(count(N, L), 0)) <=> ![N: $int, L: list] : (in(N, L) <=> (~$lesseq(count(N, L), 0)))),
% 0.13/0.40      inference(quant_intro,[status(thm)],[4])).
% 0.13/0.40  tff(6,axiom,(![N: $int, L: list] : (in(N, L) <=> $greater(count(N, L), 0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a_8')).
% 0.13/0.40  tff(7,plain,
% 0.13/0.40      (![N: $int, L: list] : (in(N, L) <=> (~$lesseq(count(N, L), 0)))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.40  tff(8,plain,
% 0.13/0.40      (![N: $int, L: list] : (in(N, L) <=> (~$lesseq(count(N, L), 0)))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[7, 3])).
% 0.13/0.40  tff(9,plain,(
% 0.13/0.40      ![N: $int, L: list] : (in(N, L) <=> (~$lesseq(count(N, L), 0)))),
% 0.13/0.40      inference(skolemize,[status(sab)],[8])).
% 0.13/0.40  tff(10,plain,
% 0.13/0.40      (![N: $int, L: list] : (in(N, L) <=> (~$lesseq(count(N, L), 0)))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[9, 2])).
% 0.13/0.40  tff(11,plain,
% 0.13/0.40      ((~![N: $int, L: list] : (in(N, L) <=> (~$lesseq(count(N, L), 0)))) | (in(A!6, nil) <=> (~$lesseq(count(A!6, nil), 0)))),
% 0.13/0.40      inference(quant_inst,[status(thm)],[])).
% 0.13/0.40  tff(12,plain,
% 0.13/0.40      (in(A!6, nil) <=> (~$lesseq(count(A!6, nil), 0))),
% 0.13/0.40      inference(unit_resolution,[status(thm)],[11, 10])).
% 0.13/0.40  tff(13,plain,
% 0.13/0.40      ((~(~in(A!6, nil))) <=> in(A!6, nil)),
% 0.13/0.40      inference(rewrite,[status(thm)],[])).
% 0.13/0.40  tff(14,plain,
% 0.13/0.40      ((~![A: $int] : (~in(A, nil))) <=> (~![A: $int] : (~in(A, nil)))),
% 0.13/0.40      inference(rewrite,[status(thm)],[])).
% 0.13/0.40  tff(15,axiom,(~![A: $int] : (~in(A, nil))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c')).
% 0.13/0.40  tff(16,plain,
% 0.13/0.40      (~![A: $int] : (~in(A, nil))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[15, 14])).
% 0.13/0.40  tff(17,plain,
% 0.13/0.40      (~![A: $int] : (~in(A, nil))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[16, 14])).
% 0.13/0.40  tff(18,plain,
% 0.13/0.40      (~![A: $int] : (~in(A, nil))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[17, 14])).
% 0.13/0.40  tff(19,plain,
% 0.13/0.40      (~![A: $int] : (~in(A, nil))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.40  tff(20,plain,
% 0.13/0.40      (~![A: $int] : (~in(A, nil))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[19, 14])).
% 0.13/0.40  tff(21,plain,
% 0.13/0.40      (~![A: $int] : (~in(A, nil))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[20, 14])).
% 0.13/0.40  tff(22,plain,
% 0.13/0.40      (~![A: $int] : (~in(A, nil))),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[21, 14])).
% 0.13/0.40  tff(23,plain,(
% 0.13/0.40      ~(~in(A!6, nil))),
% 0.13/0.40      inference(skolemize,[status(sab)],[22])).
% 0.13/0.40  tff(24,plain,
% 0.13/0.40      (in(A!6, nil)),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[23, 13])).
% 0.13/0.40  tff(25,plain,
% 0.13/0.40      ((~(in(A!6, nil) <=> (~$lesseq(count(A!6, nil), 0)))) | (~in(A!6, nil)) | (~$lesseq(count(A!6, nil), 0))),
% 0.13/0.40      inference(tautology,[status(thm)],[])).
% 0.13/0.40  tff(26,plain,
% 0.13/0.40      ((~(in(A!6, nil) <=> (~$lesseq(count(A!6, nil), 0)))) | (~$lesseq(count(A!6, nil), 0))),
% 0.13/0.40      inference(unit_resolution,[status(thm)],[25, 24])).
% 0.13/0.40  tff(27,plain,
% 0.13/0.40      (~$lesseq(count(A!6, nil), 0)),
% 0.13/0.40      inference(unit_resolution,[status(thm)],[26, 12])).
% 0.13/0.40  tff(28,plain,
% 0.13/0.40      ((~(count(A!6, nil) = 0)) | $lesseq(count(A!6, nil), 0)),
% 0.13/0.40      inference(theory_lemma,[status(thm)],[])).
% 0.13/0.40  tff(29,plain,
% 0.13/0.40      (~(count(A!6, nil) = 0)),
% 0.13/0.40      inference(unit_resolution,[status(thm)],[28, 27])).
% 0.13/0.40  tff(30,plain,
% 0.13/0.40      (^[K: $int] : refl((count(K, nil) = 0) <=> (count(K, nil) = 0))),
% 0.13/0.40      inference(bind,[status(th)],[])).
% 0.13/0.40  tff(31,plain,
% 0.13/0.40      (![K: $int] : (count(K, nil) = 0) <=> ![K: $int] : (count(K, nil) = 0)),
% 0.13/0.40      inference(quant_intro,[status(thm)],[30])).
% 0.13/0.40  tff(32,plain,
% 0.13/0.40      (![K: $int] : (count(K, nil) = 0) <=> ![K: $int] : (count(K, nil) = 0)),
% 0.13/0.40      inference(rewrite,[status(thm)],[])).
% 0.13/0.40  tff(33,axiom,(![K: $int] : (count(K, nil) = 0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','a')).
% 0.13/0.40  tff(34,plain,
% 0.13/0.40      (![K: $int] : (count(K, nil) = 0)),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[33, 32])).
% 0.13/0.40  tff(35,plain,(
% 0.13/0.40      ![K: $int] : (count(K, nil) = 0)),
% 0.13/0.40      inference(skolemize,[status(sab)],[34])).
% 0.13/0.40  tff(36,plain,
% 0.13/0.40      (![K: $int] : (count(K, nil) = 0)),
% 0.13/0.40      inference(modus_ponens,[status(thm)],[35, 31])).
% 0.13/0.40  tff(37,plain,
% 0.13/0.40      ((~![K: $int] : (count(K, nil) = 0)) | (count(A!6, nil) = 0)),
% 0.13/0.40      inference(quant_inst,[status(thm)],[])).
% 0.13/0.40  tff(38,plain,
% 0.13/0.40      ($false),
% 0.13/0.40      inference(unit_resolution,[status(thm)],[37, 36, 29])).
% 0.13/0.40  % SZS output end Proof
%------------------------------------------------------------------------------