TSTP Solution File: ITP334_1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 : Sat Sep 17 04:18:46 EDT 2022
% Result : Theorem 0.40s 0.57s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.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 : Thu Sep 1 07:20:50 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.
% 0.40/0.57 % SZS status Theorem
% 0.40/0.57 % SZS output start Proof
% 0.40/0.57 tff(tptp_fun__fun_app_h__type, type, (
% 0.40/0.57 tptp_fun__fun_app_h_: ( 'Nat_int_fun$' * 'Nat$' ) > $int)).
% 0.40/0.57 tff(tptp_fun__card___type, type, (
% 0.40/0.57 tptp_fun__card__: 'Rows_set$' > 'Nat$')).
% 0.40/0.57 tff(tptp_fun__top___type, type, (
% 0.40/0.57 tptp_fun__top__: 'Rows_set$')).
% 0.40/0.57 tff(tptp_fun__of_nat___type, type, (
% 0.40/0.57 tptp_fun__of_nat__: 'Nat_int_fun$')).
% 0.40/0.57 tff(1,plain,
% 0.40/0.57 ($lesseq($sum(0, 1), tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|))) <=> $lesseq(1, tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(2,axiom,($lesseq($sum(0, 1), tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom365')).
% 0.40/0.57 tff(3,plain,
% 0.40/0.57 ($lesseq(1, tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.40/0.57 tff(4,plain,
% 0.40/0.57 ((~(($less(tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)), $sum(0, 1)) => $less(0, tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)))) & ((~$less(tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)), $sum(0, 1))) => $less($difference(tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)), $sum(0, 1)), tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)))))) <=> (~($lesseq(1, tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|))) | (~$lesseq(tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)), 0))))),
% 0.40/0.57 inference(rewrite,[status(thm)],[])).
% 0.40/0.57 tff(5,axiom,(~(($less(tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)), $sum(0, 1)) => $less(0, tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)))) & ((~$less(tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)), $sum(0, 1))) => $less($difference(tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)), $sum(0, 1)), tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture7')).
% 0.40/0.57 tff(6,plain,
% 0.40/0.57 (~($lesseq(1, tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|))) | (~$lesseq(tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)), 0)))),
% 0.40/0.57 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.40/0.57 tff(7,plain,
% 0.40/0.57 (~$lesseq(1, tptp_fun__fun_app_h_(|'of_nat$'|, tptp_fun__card__(|'top$'|)))),
% 0.40/0.57 inference(or_elim,[status(thm)],[6])).
% 0.40/0.57 tff(8,plain,
% 0.40/0.57 ($false),
% 0.40/0.57 inference(unit_resolution,[status(thm)],[7, 3])).
% 0.40/0.57 % SZS output end Proof
%------------------------------------------------------------------------------