TSTP Solution File: ITP328_1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% 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 : n026.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 04:18:45 EDT 2022
% Result : Theorem 0.86s 0.87s
% Output : Proof 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n026.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 07:36:22 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.
% 0.86/0.87 % SZS status Theorem
% 0.86/0.87 % SZS output start Proof
% 0.86/0.87 tff(tptp_fun__fun_app_e__type, type, (
% 0.86/0.87 tptp_fun__fun_app_e_: ( 'Nat_int_fun$' * 'Nat$' ) > $int)).
% 0.86/0.87 tff(tptp_fun__to_nat___type, type, (
% 0.86/0.87 tptp_fun__to_nat__: 'N$' > 'Nat$')).
% 0.86/0.87 tff(tptp_fun__of_nat___type, type, (
% 0.86/0.87 tptp_fun__of_nat__: 'Nat_int_fun$')).
% 0.86/0.87 tff(tptp_fun__fun_app_d__type, type, (
% 0.86/0.87 tptp_fun__fun_app_d_: ( 'N_bool_fun$' * 'N$' ) > $o)).
% 0.86/0.87 tff(tptp_fun__fun_app_g__type, type, (
% 0.86/0.87 tptp_fun__fun_app_g_: ( 'N_n_bool_fun_fun$' * 'N$' ) > 'N_bool_fun$')).
% 0.86/0.87 tff(tptp_fun__less_eq___type, type, (
% 0.86/0.87 tptp_fun__less_eq__: 'N_n_bool_fun_fun$')).
% 0.86/0.87 tff(tptp_fun__x___type, type, (
% 0.86/0.87 tptp_fun__x__: 'N$')).
% 0.86/0.87 tff(tptp_fun__i___type, type, (
% 0.86/0.87 tptp_fun__i__: 'N$')).
% 0.86/0.87 tff(1,plain,
% 0.86/0.87 (^[A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : refl(((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0)) <=> ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0)))),
% 0.86/0.87 inference(bind,[status(th)],[])).
% 0.86/0.87 tff(2,plain,
% 0.86/0.87 (![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0)) <=> ![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0))),
% 0.86/0.87 inference(quant_intro,[status(thm)],[1])).
% 0.86/0.87 tff(3,plain,
% 0.86/0.87 (^[A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : rewrite(((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)))), 0)) <=> ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0)))),
% 0.86/0.87 inference(bind,[status(th)],[])).
% 0.86/0.87 tff(4,plain,
% 0.86/0.87 (![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)))), 0)) <=> ![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0))),
% 0.86/0.87 inference(quant_intro,[status(thm)],[3])).
% 0.86/0.87 tff(5,plain,
% 0.86/0.87 (^[A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : rewrite(((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)))) <=> ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)))), 0)))),
% 0.86/0.88 inference(bind,[status(th)],[])).
% 0.86/0.88 tff(6,plain,
% 0.86/0.88 (![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)))) <=> ![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)))), 0))),
% 0.86/0.88 inference(quant_intro,[status(thm)],[5])).
% 0.86/0.88 tff(7,plain,
% 0.86/0.88 (![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)))) <=> ![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1))))),
% 0.86/0.88 inference(rewrite,[status(thm)],[])).
% 0.86/0.88 tff(8,plain,
% 0.86/0.88 (^[A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : rewrite((tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1) => $lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)))) <=> ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)))))),
% 0.86/0.88 inference(bind,[status(th)],[])).
% 0.86/0.88 tff(9,plain,
% 0.86/0.88 (![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : (tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1) => $lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)))) <=> ![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1))))),
% 0.86/0.88 inference(quant_intro,[status(thm)],[8])).
% 0.86/0.88 tff(10,axiom,(![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : (tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1) => $lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom24')).
% 0.86/0.88 tff(11,plain,
% 0.86/0.88 (![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1))))),
% 0.86/0.88 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.86/0.88 tff(12,plain,
% 0.86/0.88 (![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1))))),
% 0.86/0.88 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.86/0.88 tff(13,plain,
% 0.86/0.88 (![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $lesseq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)))), 0))),
% 0.86/0.88 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.86/0.88 tff(14,plain,
% 0.86/0.88 (![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0))),
% 0.86/0.88 inference(modus_ponens,[status(thm)],[13, 4])).
% 0.86/0.88 tff(15,plain,(
% 0.86/0.88 ![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0))),
% 0.86/0.88 inference(skolemize,[status(sab)],[14])).
% 0.86/0.88 tff(16,plain,
% 0.86/0.88 (![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0))),
% 0.86/0.88 inference(modus_ponens,[status(thm)],[15, 2])).
% 0.86/0.88 tff(17,plain,
% 0.86/0.88 (tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, |'i$'|), |'x$'|) <=> tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, |'i$'|), |'x$'|)),
% 0.86/0.88 inference(rewrite,[status(thm)],[])).
% 0.86/0.88 tff(18,axiom,(tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, |'i$'|), |'x$'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom16')).
% 0.86/0.88 tff(19,plain,
% 0.86/0.88 (tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, |'i$'|), |'x$'|)),
% 0.86/0.88 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.86/0.88 tff(20,plain,
% 0.86/0.88 ((~$lesseq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)))), 0)) <=> (~$greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)))), 0))),
% 0.86/0.88 inference(rewrite,[status(thm)],[])).
% 0.86/0.88 tff(21,plain,
% 0.86/0.88 ((~$lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)))) <=> (~$lesseq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)))), 0))),
% 0.86/0.88 inference(rewrite,[status(thm)],[])).
% 0.86/0.88 tff(22,plain,
% 0.86/0.88 ((~$lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)))) <=> (~$lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|))))),
% 0.86/0.88 inference(rewrite,[status(thm)],[])).
% 0.86/0.88 tff(23,plain,
% 0.86/0.88 ((~(($less(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|))) => ($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), 0) = tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)))) & ((~$less(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)))) => ($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), $difference(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)))) = tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)))))) <=> (~($lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|))) | (tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)) = tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)))))),
% 0.86/0.88 inference(rewrite,[status(thm)],[])).
% 0.86/0.88 tff(24,axiom,(~(($less(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|))) => ($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), 0) = tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)))) & ((~$less(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)))) => ($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), $difference(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)))) = tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conjecture5')).
% 0.86/0.88 tff(25,plain,
% 0.86/0.88 (~($lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|))) | (tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)) = tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|))))),
% 0.86/0.88 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.86/0.88 tff(26,plain,
% 0.86/0.88 (~$lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)))),
% 0.86/0.88 inference(or_elim,[status(thm)],[25])).
% 0.86/0.88 tff(27,plain,
% 0.86/0.88 (~$lesseq(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)))),
% 0.86/0.88 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.86/0.88 tff(28,plain,
% 0.86/0.88 (~$lesseq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)))), 0)),
% 0.86/0.88 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.86/0.88 tff(29,plain,
% 0.86/0.88 (~$greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)))), 0)),
% 0.86/0.88 inference(modus_ponens,[status(thm)],[28, 20])).
% 0.86/0.88 tff(30,plain,
% 0.86/0.88 (((~![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0))) | ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, |'i$'|), |'x$'|)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)))), 0))) <=> ((~![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0))) | (~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, |'i$'|), |'x$'|)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)))), 0))),
% 0.86/0.88 inference(rewrite,[status(thm)],[])).
% 0.86/0.88 tff(31,plain,
% 0.86/0.88 ((~![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0))) | ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, |'i$'|), |'x$'|)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)))), 0))),
% 0.92/0.92 inference(quant_inst,[status(thm)],[])).
% 0.92/0.92 tff(32,plain,
% 0.92/0.92 ((~![A__questionmark_v0: 'N$', A__questionmark_v1: 'N$'] : ((~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, A__questionmark_v0), A__questionmark_v1)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v1)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(A__questionmark_v0)))), 0))) | (~tptp_fun__fun_app_d_(tptp_fun__fun_app_g_(|'less_eq$'|, |'i$'|), |'x$'|)) | $greatereq($sum(tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'x$'|)), $product(-1, tptp_fun__fun_app_e_(|'of_nat$'|, tptp_fun__to_nat__(|'i$'|)))), 0)),
% 0.92/0.92 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.92/0.92 tff(33,plain,
% 0.92/0.92 ($false),
% 0.92/0.92 inference(unit_resolution,[status(thm)],[32, 29, 19, 16])).
% 0.92/0.92 % SZS output end Proof
%------------------------------------------------------------------------------