%------------------------------------------------------------------------------
% 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 : n017.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 04:18:53 EDT 2022

% Result   : Theorem 0.75s 0.77s
% Output   : Proof 0.75s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.04/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n017.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 06:56:07 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.
% 0.75/0.77  % SZS status Theorem
% 0.75/0.77  % SZS output start Proof
% 0.75/0.77  tff(tptp_fun__fun_app_a__type, type, (
% 0.75/0.77     tptp_fun__fun_app_a_: ( 'Nat_int_fun$' * 'Nat$' ) > $int)).
% 0.75/0.77  tff(tptp_fun__fun_app_b__type, type, (
% 0.75/0.77     tptp_fun__fun_app_b_: ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$')).
% 0.75/0.77  tff(tptp_fun__nat___type, type, (
% 0.75/0.77     tptp_fun__nat__: $int > 'Nat$')).
% 0.75/0.77  tff(tptp_fun__n___type, type, (
% 0.75/0.77     tptp_fun__n__: 'Nat$')).
% 0.75/0.77  tff(tptp_fun__of_nat___type, type, (
% 0.75/0.77     tptp_fun__of_nat__: 'Nat_int_fun$')).
% 0.75/0.77  tff(tptp_fun__power___type, type, (
% 0.75/0.77     tptp_fun__power__: 'Nat$' > 'Nat_nat_fun$')).
% 0.75/0.77  tff(tptp_fun__size___type, type, (
% 0.75/0.77     tptp_fun__size__: 'A_ltln_list$' > 'Nat$')).
% 0.75/0.77  tff(tptp_fun__ys___type, type, (
% 0.75/0.77     tptp_fun__ys__: 'A_ltln_list$')).
% 0.75/0.77  tff(tptp_fun__zero___type, type, (
% 0.75/0.77     tptp_fun__zero__: 'Nat$')).
% 0.75/0.77  tff(1,plain,
% 0.75/0.77      (^[A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : refl(((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0))) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0))))),
% 0.75/0.77      inference(bind,[status(th)],[])).
% 0.75/0.77  tff(2,plain,
% 0.75/0.77      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0)))),
% 0.75/0.77      inference(quant_intro,[status(thm)],[1])).
% 0.75/0.77  tff(3,plain,
% 0.75/0.77      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0)))),
% 0.75/0.77      inference(rewrite,[status(thm)],[])).
% 0.75/0.77  tff(4,plain,
% 0.75/0.77      (^[A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : rewrite(($less(0, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1))) <=> ($less(0, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0))) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0))))),
% 0.75/0.77      inference(bind,[status(th)],[])).
% 0.75/0.77  tff(5,plain,
% 0.75/0.77      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ($less(0, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1))) <=> ($less(0, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0)))),
% 0.75/0.77      inference(quant_intro,[status(thm)],[4])).
% 0.75/0.77  tff(6,axiom,(![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ($less(0, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1))) <=> ($less(0, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom383')).
% 0.75/0.77  tff(7,plain,
% 0.75/0.77      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0)))),
% 0.75/0.77      inference(modus_ponens,[status(thm)],[6, 5])).
% 0.75/0.77  tff(8,plain,
% 0.75/0.77      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0)))),
% 0.75/0.77      inference(modus_ponens,[status(thm)],[7, 3])).
% 0.75/0.77  tff(9,plain,(
% 0.75/0.77      ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0)))),
% 0.75/0.77      inference(skolemize,[status(sab)],[8])).
% 0.75/0.77  tff(10,plain,
% 0.75/0.77      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0)))),
% 0.75/0.77      inference(modus_ponens,[status(thm)],[9, 2])).
% 0.75/0.77  tff(11,plain,
% 0.75/0.77      ((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1) = 0)))) | ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))))) = 0)))),
% 0.75/0.77      inference(quant_inst,[status(thm)],[])).
% 0.75/0.77  tff(12,plain,
% 0.75/0.77      ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))))) = 0))),
% 0.75/0.77      inference(unit_resolution,[status(thm)],[11, 10])).
% 0.75/0.77  tff(13,plain,
% 0.75/0.77      (^[A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : refl(((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0)) <=> ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0)))),
% 0.75/0.77      inference(bind,[status(th)],[])).
% 0.75/0.77  tff(14,plain,
% 0.75/0.77      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0)) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))),
% 0.75/0.77      inference(quant_intro,[status(thm)],[13])).
% 0.75/0.77  tff(15,plain,
% 0.75/0.77      (^[A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : trans(monotonicity(trans(monotonicity(rewrite(((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))) <=> (~($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0)))), ((~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0)))) <=> (~(~($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0)))))), rewrite((~(~($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0)))) <=> ($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))), ((~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0)))) <=> ($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0)))), (((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))))) <=> ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | ($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))))), rewrite(((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | ($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))) <=> ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))), (((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))))) <=> ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))))),
% 0.75/0.77      inference(bind,[status(th)],[])).
% 0.75/0.77  tff(16,plain,
% 0.75/0.77      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))),
% 0.75/0.77      inference(quant_intro,[status(thm)],[15])).
% 0.75/0.77  tff(17,plain,
% 0.75/0.77      (^[A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : rewrite(((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)))), 0))))) <=> ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))))))),
% 0.75/0.77      inference(bind,[status(th)],[])).
% 0.75/0.77  tff(18,plain,
% 0.75/0.77      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)))), 0))))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0)))))),
% 0.75/0.77      inference(quant_intro,[status(thm)],[17])).
% 0.75/0.77  tff(19,plain,
% 0.75/0.77      (^[A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : rewrite(((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1))))))) <=> ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)))), 0))))))),
% 0.75/0.78      inference(bind,[status(th)],[])).
% 0.75/0.78  tff(20,plain,
% 0.75/0.78      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1))))))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)))), 0)))))),
% 0.75/0.78      inference(quant_intro,[status(thm)],[19])).
% 0.75/0.78  tff(21,plain,
% 0.75/0.78      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1))))))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)))))))),
% 0.75/0.78      inference(rewrite,[status(thm)],[])).
% 0.75/0.78  tff(22,plain,
% 0.75/0.78      (^[A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : trans(monotonicity(rewrite(($less(0, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0)) & $less(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)))))), rewrite($less(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2)) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1)))), ((($less(0, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0)) & $less(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))) => $less(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2))) <=> (((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1))))) => (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1)))))), rewrite((((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1))))) => (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1)))) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)))))))), ((($less(0, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0)) & $less(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))) => $less(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2))) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)))))))))),
% 0.75/0.78      inference(bind,[status(th)],[])).
% 0.75/0.78  tff(23,plain,
% 0.75/0.78      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : (($less(0, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0)) & $less(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))) => $less(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)))))))),
% 0.75/0.78      inference(quant_intro,[status(thm)],[22])).
% 0.75/0.78  tff(24,axiom,(![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : (($less(0, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0)) & $less(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))) => $less(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom585')).
% 0.75/0.78  tff(25,plain,
% 0.75/0.78      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)))))))),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[24, 23])).
% 0.75/0.78  tff(26,plain,
% 0.75/0.78      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)))))))),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[25, 21])).
% 0.75/0.78  tff(27,plain,
% 0.75/0.78      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)))), 0)))))),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[26, 20])).
% 0.75/0.78  tff(28,plain,
% 0.75/0.78      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0)))))),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[27, 18])).
% 0.75/0.78  tff(29,plain,(
% 0.75/0.78      ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0)) & (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0)))))),
% 0.75/0.78      inference(skolemize,[status(sab)],[28])).
% 0.75/0.78  tff(30,plain,
% 0.75/0.78      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[29, 16])).
% 0.75/0.78  tff(31,plain,
% 0.75/0.78      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[30, 14])).
% 0.75/0.78  tff(32,plain,
% 0.75/0.78      ($lesseq($sum($product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|))), 0) <=> $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)))), 0)),
% 0.75/0.78      inference(rewrite,[status(thm)],[])).
% 0.75/0.78  tff(33,plain,
% 0.75/0.78      ($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))) = $sum($product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)))),
% 0.75/0.78      inference(rewrite,[status(thm)],[])).
% 0.75/0.78  tff(34,plain,
% 0.75/0.78      ($lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))), 0) <=> $lesseq($sum($product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|))), 0)),
% 0.75/0.78      inference(monotonicity,[status(thm)],[33])).
% 0.75/0.78  tff(35,plain,
% 0.75/0.78      ($lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))), 0) <=> $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)))), 0)),
% 0.75/0.78      inference(transitivity,[status(thm)],[34, 32])).
% 0.75/0.78  tff(36,plain,
% 0.75/0.78      ($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)) <=> $lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))), 0)),
% 0.75/0.78      inference(rewrite,[status(thm)],[])).
% 0.75/0.78  tff(37,plain,
% 0.75/0.78      ($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)) <=> $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))),
% 0.75/0.78      inference(rewrite,[status(thm)],[])).
% 0.75/0.78  tff(38,axiom,($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom2')).
% 0.75/0.78  tff(39,plain,
% 0.75/0.78      ($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[38, 37])).
% 0.75/0.78  tff(40,plain,
% 0.75/0.78      ($lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))), 0)),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[39, 36])).
% 0.75/0.78  tff(41,plain,
% 0.75/0.78      ($greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)))), 0)),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[40, 35])).
% 0.75/0.78  tff(42,plain,
% 0.75/0.78      ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))) <=> (~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))), 0))),
% 0.75/0.78      inference(rewrite,[status(thm)],[])).
% 0.75/0.78  tff(43,plain,
% 0.75/0.78      (tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))) = tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))),
% 0.75/0.78      inference(rewrite,[status(thm)],[])).
% 0.75/0.78  tff(44,plain,
% 0.75/0.78      (tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))) = tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))))),
% 0.75/0.78      inference(monotonicity,[status(thm)],[43])).
% 0.75/0.78  tff(45,plain,
% 0.75/0.78      (tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))))) = tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))),
% 0.75/0.78      inference(monotonicity,[status(thm)],[44])).
% 0.75/0.78  tff(46,plain,
% 0.75/0.78      (tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))) = tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))))))),
% 0.75/0.78      inference(monotonicity,[status(thm)],[45])).
% 0.75/0.78  tff(47,plain,
% 0.75/0.78      (tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|) = tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)),
% 0.75/0.78      inference(monotonicity,[status(thm)],[46])).
% 0.75/0.78  tff(48,plain,
% 0.75/0.78      (tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)) = tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|))),
% 0.75/0.78      inference(monotonicity,[status(thm)],[47])).
% 0.75/0.78  tff(49,plain,
% 0.75/0.78      (tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|)) = tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))),
% 0.75/0.78      inference(monotonicity,[status(thm)],[46])).
% 0.75/0.78  tff(50,plain,
% 0.75/0.78      (tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))) = tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|)))),
% 0.75/0.78      inference(monotonicity,[status(thm)],[49])).
% 0.75/0.78  tff(51,plain,
% 0.75/0.78      ($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|))) <=> $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))),
% 0.75/0.78      inference(monotonicity,[status(thm)],[50, 48])).
% 0.75/0.78  tff(52,plain,
% 0.75/0.78      ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|))))),
% 0.75/0.78      inference(monotonicity,[status(thm)],[51])).
% 0.75/0.78  tff(53,plain,
% 0.75/0.78      ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|))))),
% 0.75/0.78      inference(rewrite,[status(thm)],[])).
% 0.75/0.78  tff(54,plain,
% 0.75/0.78      ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), 1))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), 1))))), |'n$'|)))) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|))))),
% 0.75/0.78      inference(rewrite,[status(thm)],[])).
% 0.75/0.78  tff(55,axiom,(~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), 1))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), 1))))), |'n$'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','conjecture1')).
% 0.75/0.78  tff(56,plain,
% 0.75/0.78      (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[55, 54])).
% 0.75/0.78  tff(57,plain,
% 0.75/0.78      (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[56, 53])).
% 0.75/0.78  tff(58,plain,
% 0.75/0.78      (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[57, 52])).
% 0.75/0.78  tff(59,plain,
% 0.75/0.78      (~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))), 0)),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[58, 42])).
% 0.75/0.78  tff(60,plain,
% 0.75/0.78      (((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))) | ((~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0) | $lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))), 0))) <=> ((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))) | (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0) | $lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))), 0))),
% 0.75/0.78      inference(rewrite,[status(thm)],[])).
% 0.75/0.78  tff(61,plain,
% 0.75/0.78      (((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))))), 0)) <=> ((~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0) | $lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))), 0))),
% 0.75/0.78      inference(rewrite,[status(thm)],[])).
% 0.75/0.78  tff(62,plain,
% 0.75/0.78      (((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))) | ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))))), 0))) <=> ((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))) | ((~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0) | $lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))), 0)))),
% 0.75/0.78      inference(monotonicity,[status(thm)],[61])).
% 0.75/0.78  tff(63,plain,
% 0.75/0.78      (((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))) | ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))))), 0))) <=> ((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))) | (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0) | $lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))), 0))),
% 0.75/0.78      inference(transitivity,[status(thm)],[62, 60])).
% 0.75/0.78  tff(64,plain,
% 0.75/0.78      ((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))) | ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))))), 0))),
% 0.75/0.78      inference(quant_inst,[status(thm)],[])).
% 0.75/0.78  tff(65,plain,
% 0.75/0.78      ((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$', A__questionmark_v2: 'Nat$'] : ((~$lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v2), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v0), 0) | $greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1)), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v2)))), 0))) | (~$greatereq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__size__(|'ys$'|)))), 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0) | $lesseq($sum(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), tptp_fun__size__(|'ys$'|))), $product(-1, tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), |'n$'|)))), 0)),
% 0.75/0.78      inference(modus_ponens,[status(thm)],[64, 63])).
% 0.75/0.78  tff(66,plain,
% 0.75/0.78      ($lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0)),
% 0.75/0.78      inference(unit_resolution,[status(thm)],[65, 59, 41, 31])).
% 0.75/0.78  tff(67,plain,
% 0.75/0.78      ((~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0)) <=> ((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))))) = 0)))) | (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|)))))), 0)) | (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))))) = 0)))),
% 0.75/0.78      inference(tautology,[status(thm)],[])).
% 0.75/0.78  tff(68,plain,
% 0.75/0.78      (~((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))))) = 0))),
% 0.75/0.78      inference(unit_resolution,[status(thm)],[67, 66, 12])).
% 0.75/0.79  tff(69,plain,
% 0.75/0.79      (^[A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : refl(((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0)))) <=> ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0)))))),
% 0.75/0.79      inference(bind,[status(th)],[])).
% 0.75/0.79  tff(70,plain,
% 0.75/0.79      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0)))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))),
% 0.75/0.79      inference(quant_intro,[status(thm)],[69])).
% 0.75/0.79  tff(71,plain,
% 0.75/0.79      (^[A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : rewrite(((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> ((A__questionmark_v0 = |'zero$'|) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0)))) <=> ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0)))))),
% 0.75/0.79      inference(bind,[status(th)],[])).
% 0.75/0.79  tff(72,plain,
% 0.75/0.79      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> ((A__questionmark_v0 = |'zero$'|) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0)))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))),
% 0.75/0.79      inference(quant_intro,[status(thm)],[71])).
% 0.75/0.79  tff(73,plain,
% 0.75/0.79      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> ((A__questionmark_v0 = |'zero$'|) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0)))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> ((A__questionmark_v0 = |'zero$'|) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))),
% 0.75/0.79      inference(rewrite,[status(thm)],[])).
% 0.75/0.79  tff(74,plain,
% 0.75/0.79      (^[A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : rewrite(((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> ((A__questionmark_v0 = |'zero$'|) & $less(0, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1)))) <=> ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> ((A__questionmark_v0 = |'zero$'|) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0)))))),
% 0.75/0.79      inference(bind,[status(th)],[])).
% 0.75/0.79  tff(75,plain,
% 0.75/0.79      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> ((A__questionmark_v0 = |'zero$'|) & $less(0, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1)))) <=> ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> ((A__questionmark_v0 = |'zero$'|) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))),
% 0.75/0.79      inference(quant_intro,[status(thm)],[74])).
% 0.75/0.79  tff(76,axiom,(![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> ((A__questionmark_v0 = |'zero$'|) & $less(0, tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom385')).
% 0.75/0.79  tff(77,plain,
% 0.75/0.79      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> ((A__questionmark_v0 = |'zero$'|) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))),
% 0.75/0.79      inference(modus_ponens,[status(thm)],[76, 75])).
% 0.75/0.79  tff(78,plain,
% 0.75/0.79      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> ((A__questionmark_v0 = |'zero$'|) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))),
% 0.75/0.79      inference(modus_ponens,[status(thm)],[77, 73])).
% 0.75/0.79  tff(79,plain,(
% 0.75/0.79      ![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> ((A__questionmark_v0 = |'zero$'|) & (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))),
% 0.75/0.79      inference(skolemize,[status(sab)],[78])).
% 0.75/0.79  tff(80,plain,
% 0.75/0.79      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))),
% 0.75/0.79      inference(modus_ponens,[status(thm)],[79, 72])).
% 0.75/0.79  tff(81,plain,
% 0.75/0.79      (![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))),
% 0.75/0.79      inference(modus_ponens,[status(thm)],[80, 70])).
% 0.75/0.79  tff(82,plain,
% 0.75/0.79      (((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))) | ((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)))) <=> ((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))) | ((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0))))),
% 0.75/0.79      inference(rewrite,[status(thm)],[])).
% 0.75/0.79  tff(83,plain,
% 0.75/0.79      (((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~((~(|'zero$'| = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)))) <=> ((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)))),
% 0.75/0.79      inference(rewrite,[status(thm)],[])).
% 0.75/0.79  tff(84,plain,
% 0.75/0.79      (((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))) | ((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~((~(|'zero$'| = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0))))) <=> ((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))) | ((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0))))),
% 0.75/0.79      inference(monotonicity,[status(thm)],[83])).
% 0.75/0.79  tff(85,plain,
% 0.75/0.79      (((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))) | ((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~((~(|'zero$'| = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0))))) <=> ((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))) | ((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0))))),
% 0.75/0.79      inference(transitivity,[status(thm)],[84, 82])).
% 0.75/0.79  tff(86,plain,
% 0.75/0.79      ((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))) | ((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~((~(|'zero$'| = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0))))),
% 0.75/0.79      inference(quant_inst,[status(thm)],[])).
% 0.75/0.79  tff(87,plain,
% 0.75/0.79      ((~![A__questionmark_v0: 'Nat$', A__questionmark_v1: 'Nat$'] : ((tptp_fun__fun_app_b_(tptp_fun__power__(A__questionmark_v0), A__questionmark_v1) = |'zero$'|) <=> (~((~(A__questionmark_v0 = |'zero$'|)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, A__questionmark_v1), 0))))) | ((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)))),
% 0.75/0.79      inference(modus_ponens,[status(thm)],[86, 85])).
% 0.75/0.79  tff(88,plain,
% 0.75/0.79      ((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0))),
% 0.75/0.79      inference(unit_resolution,[status(thm)],[87, 81])).
% 0.75/0.79  tff(89,plain,
% 0.75/0.79      ((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|)),
% 0.75/0.79      inference(rewrite,[status(thm)],[])).
% 0.75/0.79  tff(90,axiom,(tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom325')).
% 0.75/0.79  tff(91,plain,
% 0.75/0.79      (tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|),
% 0.75/0.79      inference(modus_ponens,[status(thm)],[90, 89])).
% 0.75/0.79  tff(92,plain,
% 0.75/0.79      ((~((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)))) | (~(tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|)) | (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0))),
% 0.75/0.79      inference(tautology,[status(thm)],[])).
% 0.75/0.79  tff(93,plain,
% 0.75/0.79      ((~((tptp_fun__fun_app_b_(tptp_fun__power__(|'zero$'|), tptp_fun__nat__(2)) = |'zero$'|) <=> (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)))) | (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0))),
% 0.75/0.79      inference(unit_resolution,[status(thm)],[92, 91])).
% 0.75/0.79  tff(94,plain,
% 0.75/0.79      (~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)),
% 0.75/0.79      inference(unit_resolution,[status(thm)],[93, 88])).
% 0.75/0.79  tff(95,plain,
% 0.75/0.79      (((~$lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)) | (tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__fun_app_b_(tptp_fun__power__(tptp_fun__nat__(2)), tptp_fun__nat__($sum(1, tptp_fun__fun_app_a_(|'of_nat$'|, |'n$'|))))) = 0)) | $lesseq(tptp_fun__fun_app_a_(|'of_nat$'|, tptp_fun__nat__(2)), 0)),
% 0.75/0.83      inference(tautology,[status(thm)],[])).
% 0.75/0.83  tff(96,plain,
% 0.75/0.83      ($false),
% 0.75/0.83      inference(unit_resolution,[status(thm)],[95, 94, 68])).
% 0.75/0.83  % SZS output end Proof
%------------------------------------------------------------------------------