%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SYO661-1 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n006.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 30 01:41:13 EDT 2022

% Result   : Unsatisfiable 11.46s 7.63s
% Output   : Proof 11.46s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO661-1 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34  % Computer : n006.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Mon Sep  5 15:44:38 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35  Usage: tptp [options] [-file:]file
% 0.14/0.35    -h, -?       prints this message.
% 0.14/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.14/0.35    -m, -model   generate model.
% 0.14/0.35    -p, -proof   generate proof.
% 0.14/0.35    -c, -core    generate unsat core of named formulas.
% 0.14/0.35    -st, -statistics display statistics.
% 0.14/0.35    -t:timeout   set timeout (in second).
% 0.14/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.14/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35    -<param>:<value> configuration parameter and value.
% 0.14/0.35    -o:<output-file> file to place output in.
% 11.46/7.63  % SZS status Unsatisfiable
% 11.46/7.63  % SZS output start Proof
% 11.46/7.63  tff(tptp_fun__E__type, type, (
% 11.46/7.63     tptp_fun__E_: ( $i * $i ) > $o)).
% 11.46/7.63  tff(f_type, type, (
% 11.46/7.63     f: $i > $i)).
% 11.46/7.63  tff(suc_type, type, (
% 11.46/7.63     suc: $i > $i)).
% 11.46/7.63  tff(z_type, type, (
% 11.46/7.63     z: $i)).
% 11.46/7.63  tff(s_type, type, (
% 11.46/7.63     s: $i > $i)).
% 11.46/7.63  tff(tptp_fun__0__type, type, (
% 11.46/7.63     tptp_fun__0_: $i)).
% 11.46/7.63  tff(tptp_fun__LE__type, type, (
% 11.46/7.63     tptp_fun__LE_: ( $i * $i ) > $o)).
% 11.46/7.63  tff(iLEQ_type, type, (
% 11.46/7.63     iLEQ: ( $i * $i ) > $o)).
% 11.46/7.63  tff(1,assumption,(~tptp_fun__E_(f(z), f(suc(z)))), introduced(assumption)).
% 11.46/7.63  tff(2,plain,
% 11.46/7.63      (^[A: $i] : refl(tptp_fun__LE_(f(A), s(s(|'0'|))) <=> tptp_fun__LE_(f(A), s(s(|'0'|))))),
% 11.46/7.63      inference(bind,[status(th)],[])).
% 11.46/7.63  tff(3,plain,
% 11.46/7.63      (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 11.46/7.63      inference(quant_intro,[status(thm)],[2])).
% 11.46/7.63  tff(4,plain,
% 11.46/7.63      (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 11.46/7.63      inference(rewrite,[status(thm)],[])).
% 11.46/7.63  tff(5,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_72')).
% 11.46/7.63  tff(6,plain,
% 11.46/7.63      (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[5, 4])).
% 11.46/7.63  tff(7,plain,(
% 11.46/7.63      ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 11.46/7.63      inference(skolemize,[status(sab)],[6])).
% 11.46/7.63  tff(8,plain,
% 11.46/7.63      (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[7, 3])).
% 11.46/7.63  tff(9,plain,
% 11.46/7.63      ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 11.46/7.63      inference(quant_inst,[status(thm)],[])).
% 11.46/7.63  tff(10,plain,
% 11.46/7.63      (tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 11.46/7.63      inference(unit_resolution,[status(thm)],[9, 8])).
% 11.46/7.63  tff(11,assumption,(~tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 11.46/7.63  tff(12,plain,
% 11.46/7.63      (^[B_10: $i] : refl((tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))) <=> (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))))),
% 11.46/7.63      inference(bind,[status(th)],[])).
% 11.46/7.63  tff(13,plain,
% 11.46/7.63      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 11.46/7.63      inference(quant_intro,[status(thm)],[12])).
% 11.46/7.63  tff(14,plain,
% 11.46/7.63      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 11.46/7.63      inference(rewrite,[status(thm)],[])).
% 11.46/7.63  tff(15,plain,
% 11.46/7.63      (^[B_10: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))) | tptp_fun__LE_(f(B_10), s(|'0'|))) <=> (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))))),
% 11.46/7.63      inference(bind,[status(th)],[])).
% 11.46/7.63  tff(16,plain,
% 11.46/7.63      (![B_10: $i] : (((~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))) | tptp_fun__LE_(f(B_10), s(|'0'|))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 11.46/7.63      inference(quant_intro,[status(thm)],[15])).
% 11.46/7.63  tff(17,axiom,(![B_10: $i] : (((~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))) | tptp_fun__LE_(f(B_10), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_119')).
% 11.46/7.63  tff(18,plain,
% 11.46/7.63      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[17, 16])).
% 11.46/7.63  tff(19,plain,
% 11.46/7.63      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[18, 14])).
% 11.46/7.63  tff(20,plain,(
% 11.46/7.63      ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 11.46/7.63      inference(skolemize,[status(sab)],[19])).
% 11.46/7.63  tff(21,plain,
% 11.46/7.63      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[20, 13])).
% 11.46/7.63  tff(22,plain,
% 11.46/7.63      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 11.46/7.63      inference(rewrite,[status(thm)],[])).
% 11.46/7.63  tff(23,plain,
% 11.46/7.63      ((tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))) <=> (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 11.46/7.63      inference(rewrite,[status(thm)],[])).
% 11.46/7.63  tff(24,plain,
% 11.46/7.63      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))))),
% 11.46/7.63      inference(monotonicity,[status(thm)],[23])).
% 11.46/7.63  tff(25,plain,
% 11.46/7.63      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 11.46/7.63      inference(transitivity,[status(thm)],[24, 22])).
% 11.46/7.63  tff(26,plain,
% 11.46/7.63      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 11.46/7.63      inference(quant_inst,[status(thm)],[])).
% 11.46/7.63  tff(27,plain,
% 11.46/7.63      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[26, 25])).
% 11.46/7.63  tff(28,plain,
% 11.46/7.63      (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 11.46/7.63      inference(unit_resolution,[status(thm)],[27, 21])).
% 11.46/7.63  tff(29,plain,
% 11.46/7.63      (tptp_fun__LE_(f(z), s(|'0'|))),
% 11.46/7.63      inference(unit_resolution,[status(thm)],[28, 11, 10])).
% 11.46/7.63  tff(30,plain,
% 11.46/7.63      (^[B_17: $i] : refl((tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|)))) <=> (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|)))))),
% 11.46/7.63      inference(bind,[status(th)],[])).
% 11.46/7.63  tff(31,plain,
% 11.46/7.63      (![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|)))) <=> ![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 11.46/7.63      inference(quant_intro,[status(thm)],[30])).
% 11.46/7.63  tff(32,plain,
% 11.46/7.63      (![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|)))) <=> ![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 11.46/7.63      inference(rewrite,[status(thm)],[])).
% 11.46/7.63  tff(33,plain,
% 11.46/7.63      (^[B_17: $i] : rewrite((((~tptp_fun__LE_(f(B_17), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_17))) | tptp_fun__LE_(f(B_17), |'0'|)) <=> (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|)))))),
% 11.46/7.63      inference(bind,[status(th)],[])).
% 11.46/7.63  tff(34,plain,
% 11.46/7.63      (![B_17: $i] : (((~tptp_fun__LE_(f(B_17), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_17))) | tptp_fun__LE_(f(B_17), |'0'|)) <=> ![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 11.46/7.63      inference(quant_intro,[status(thm)],[33])).
% 11.46/7.63  tff(35,axiom,(![B_17: $i] : (((~tptp_fun__LE_(f(B_17), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_17))) | tptp_fun__LE_(f(B_17), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_0')).
% 11.46/7.63  tff(36,plain,
% 11.46/7.63      (![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[35, 34])).
% 11.46/7.63  tff(37,plain,
% 11.46/7.63      (![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[36, 32])).
% 11.46/7.63  tff(38,plain,(
% 11.46/7.63      ![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 11.46/7.63      inference(skolemize,[status(sab)],[37])).
% 11.46/7.63  tff(39,plain,
% 11.46/7.63      (![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[38, 31])).
% 11.46/7.63  tff(40,plain,
% 11.46/7.63      ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 11.46/7.63      inference(rewrite,[status(thm)],[])).
% 11.46/7.63  tff(41,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_93')).
% 11.46/7.63  tff(42,plain,
% 11.46/7.63      (~tptp_fun__LE_(f(z), |'0'|)),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[41, 40])).
% 11.46/7.63  tff(43,plain,
% 11.46/7.63      (((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 11.46/7.63      inference(rewrite,[status(thm)],[])).
% 11.46/7.63  tff(44,plain,
% 11.46/7.63      ((tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|)))) <=> (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 11.46/7.63      inference(rewrite,[status(thm)],[])).
% 11.46/7.63  tff(45,plain,
% 11.46/7.63      (((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))))),
% 11.46/7.63      inference(monotonicity,[status(thm)],[44])).
% 11.46/7.63  tff(46,plain,
% 11.46/7.63      (((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 11.46/7.63      inference(transitivity,[status(thm)],[45, 43])).
% 11.46/7.63  tff(47,plain,
% 11.46/7.63      ((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 11.46/7.63      inference(quant_inst,[status(thm)],[])).
% 11.46/7.63  tff(48,plain,
% 11.46/7.63      ((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[47, 46])).
% 11.46/7.63  tff(49,plain,
% 11.46/7.63      (tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))),
% 11.46/7.63      inference(unit_resolution,[status(thm)],[48, 42, 39])).
% 11.46/7.63  tff(50,plain,
% 11.46/7.63      (tptp_fun__E_(|'0'|, f(z))),
% 11.46/7.63      inference(unit_resolution,[status(thm)],[49, 29])).
% 11.46/7.63  tff(51,plain,
% 11.46/7.63      (^[B_10: $i] : refl((tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))) <=> (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))))),
% 11.46/7.63      inference(bind,[status(th)],[])).
% 11.46/7.63  tff(52,plain,
% 11.46/7.63      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 11.46/7.63      inference(quant_intro,[status(thm)],[51])).
% 11.46/7.63  tff(53,plain,
% 11.46/7.63      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 11.46/7.63      inference(rewrite,[status(thm)],[])).
% 11.46/7.63  tff(54,plain,
% 11.46/7.63      (^[B_10: $i] : rewrite((((~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))) | tptp_fun__LE_(f(B_10), s(|'0'|))) <=> (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))))),
% 11.46/7.63      inference(bind,[status(th)],[])).
% 11.46/7.63  tff(55,plain,
% 11.46/7.63      (![B_10: $i] : (((~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))) | tptp_fun__LE_(f(B_10), s(|'0'|))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 11.46/7.63      inference(quant_intro,[status(thm)],[54])).
% 11.46/7.63  tff(56,axiom,(![B_10: $i] : (((~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))) | tptp_fun__LE_(f(B_10), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_118')).
% 11.46/7.63  tff(57,plain,
% 11.46/7.63      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[56, 55])).
% 11.46/7.63  tff(58,plain,
% 11.46/7.63      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[57, 53])).
% 11.46/7.63  tff(59,plain,(
% 11.46/7.63      ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 11.46/7.63      inference(skolemize,[status(sab)],[58])).
% 11.46/7.63  tff(60,plain,
% 11.46/7.63      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[59, 52])).
% 11.46/7.63  tff(61,plain,
% 11.46/7.63      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 11.46/7.63      inference(rewrite,[status(thm)],[])).
% 11.46/7.63  tff(62,plain,
% 11.46/7.63      ((tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))) <=> (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 11.46/7.63      inference(rewrite,[status(thm)],[])).
% 11.46/7.63  tff(63,plain,
% 11.46/7.63      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))))),
% 11.46/7.63      inference(monotonicity,[status(thm)],[62])).
% 11.46/7.63  tff(64,plain,
% 11.46/7.63      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 11.46/7.63      inference(transitivity,[status(thm)],[63, 61])).
% 11.46/7.63  tff(65,plain,
% 11.46/7.63      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 11.46/7.63      inference(quant_inst,[status(thm)],[])).
% 11.46/7.63  tff(66,plain,
% 11.46/7.63      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[65, 64])).
% 11.46/7.63  tff(67,plain,
% 11.46/7.63      (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 11.46/7.63      inference(unit_resolution,[status(thm)],[66, 60])).
% 11.46/7.63  tff(68,plain,
% 11.46/7.63      (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 11.46/7.63      inference(unit_resolution,[status(thm)],[67, 11, 10])).
% 11.46/7.63  tff(69,plain,
% 11.46/7.63      (^[B_17: $i] : refl((tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|)))) <=> (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|)))))),
% 11.46/7.63      inference(bind,[status(th)],[])).
% 11.46/7.63  tff(70,plain,
% 11.46/7.63      (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|)))) <=> ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 11.46/7.63      inference(quant_intro,[status(thm)],[69])).
% 11.46/7.63  tff(71,plain,
% 11.46/7.63      (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|)))) <=> ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 11.46/7.63      inference(rewrite,[status(thm)],[])).
% 11.46/7.63  tff(72,plain,
% 11.46/7.63      (^[B_17: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_17)))) | tptp_fun__LE_(f(B_17), |'0'|)) <=> (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|)))))),
% 11.46/7.63      inference(bind,[status(th)],[])).
% 11.46/7.63  tff(73,plain,
% 11.46/7.63      (![B_17: $i] : (((~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_17)))) | tptp_fun__LE_(f(B_17), |'0'|)) <=> ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 11.46/7.63      inference(quant_intro,[status(thm)],[72])).
% 11.46/7.63  tff(74,axiom,(![B_17: $i] : (((~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_17)))) | tptp_fun__LE_(f(B_17), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_57')).
% 11.46/7.63  tff(75,plain,
% 11.46/7.63      (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[74, 73])).
% 11.46/7.63  tff(76,plain,
% 11.46/7.63      (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 11.46/7.63      inference(modus_ponens,[status(thm)],[75, 71])).
% 11.46/7.64  tff(77,plain,(
% 11.46/7.64      ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 11.46/7.64      inference(skolemize,[status(sab)],[76])).
% 11.46/7.64  tff(78,plain,
% 11.46/7.64      (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 11.46/7.64      inference(modus_ponens,[status(thm)],[77, 70])).
% 11.46/7.64  tff(79,plain,
% 11.46/7.64      (((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))) <=> ((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 11.46/7.64      inference(rewrite,[status(thm)],[])).
% 11.46/7.64  tff(80,plain,
% 11.46/7.64      ((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 11.46/7.64      inference(quant_inst,[status(thm)],[])).
% 11.46/7.64  tff(81,plain,
% 11.46/7.64      ((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 11.46/7.64      inference(modus_ponens,[status(thm)],[80, 79])).
% 11.46/7.64  tff(82,plain,
% 11.46/7.64      (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 11.46/7.64      inference(unit_resolution,[status(thm)],[81, 42, 78])).
% 11.46/7.64  tff(83,plain,
% 11.46/7.64      (tptp_fun__E_(|'0'|, f(suc(z)))),
% 11.46/7.64      inference(unit_resolution,[status(thm)],[82, 68])).
% 11.46/7.64  tff(84,assumption,(tptp_fun__E_(|'0'|, f(suc(z)))), introduced(assumption)).
% 11.46/7.64  tff(85,assumption,(tptp_fun__E_(|'0'|, f(z))), introduced(assumption)).
% 11.46/7.64  tff(86,plain,
% 11.46/7.64      (^[A_2: $i] : refl((iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))),
% 11.46/7.64      inference(bind,[status(th)],[])).
% 11.46/7.64  tff(87,plain,
% 11.46/7.64      (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(quant_intro,[status(thm)],[86])).
% 11.46/7.64  tff(88,plain,
% 11.46/7.64      (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(rewrite,[status(thm)],[])).
% 11.46/7.64  tff(89,plain,
% 11.46/7.64      (^[A_2: $i] : trans(monotonicity(rewrite((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) <=> (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> ((tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))))), rewrite(((tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))) <=> (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))))),
% 11.46/7.64      inference(bind,[status(th)],[])).
% 11.46/7.64  tff(90,plain,
% 11.46/7.64      (![A_2: $i] : ((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(quant_intro,[status(thm)],[89])).
% 11.46/7.64  tff(91,axiom,(![A_2: $i] : ((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_109')).
% 11.46/7.64  tff(92,plain,
% 11.46/7.64      (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(modus_ponens,[status(thm)],[91, 90])).
% 11.46/7.64  tff(93,plain,
% 11.46/7.64      (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(modus_ponens,[status(thm)],[92, 88])).
% 11.46/7.64  tff(94,plain,(
% 11.46/7.64      ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(skolemize,[status(sab)],[93])).
% 11.46/7.64  tff(95,plain,
% 11.46/7.64      (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(modus_ponens,[status(thm)],[94, 87])).
% 11.46/7.64  tff(96,plain,
% 11.46/7.64      (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 11.46/7.64      inference(rewrite,[status(thm)],[])).
% 11.46/7.64  tff(97,plain,
% 11.46/7.64      ((iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 11.46/7.64      inference(rewrite,[status(thm)],[])).
% 11.46/7.64  tff(98,plain,
% 11.46/7.64      (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z)))))),
% 11.46/7.64      inference(monotonicity,[status(thm)],[97])).
% 11.46/7.64  tff(99,plain,
% 11.46/7.64      (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 11.46/7.64      inference(transitivity,[status(thm)],[98, 96])).
% 11.46/7.64  tff(100,plain,
% 11.46/7.64      ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 11.46/7.64      inference(quant_inst,[status(thm)],[])).
% 11.46/7.64  tff(101,plain,
% 11.46/7.64      ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 11.46/7.64      inference(modus_ponens,[status(thm)],[100, 99])).
% 11.46/7.64  tff(102,plain,
% 11.46/7.64      ((~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 11.46/7.64      inference(unit_resolution,[status(thm)],[101, 95])).
% 11.46/7.64  tff(103,plain,
% 11.46/7.64      (iLEQ(suc(z), suc(z))),
% 11.46/7.64      inference(unit_resolution,[status(thm)],[102, 1, 85, 84])).
% 11.46/7.64  tff(104,plain,
% 11.46/7.64      (^[B_18: $i, A_2: $i, B_19: $i] : refl((tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))),
% 11.46/7.64      inference(bind,[status(th)],[])).
% 11.46/7.64  tff(105,plain,
% 11.46/7.64      (![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(quant_intro,[status(thm)],[104])).
% 11.46/7.64  tff(106,plain,
% 11.46/7.64      (![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(rewrite,[status(thm)],[])).
% 11.46/7.64  tff(107,plain,
% 11.46/7.64      (^[B_18: $i, A_2: $i, B_19: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(B_18), suc(B_19)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(B_18), suc(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), (((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(B_19)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(B_18)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_18)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) <=> (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) <=> (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) <=> ((tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(B_18), f(suc(B_18)))))), rewrite(((tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) <=> (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) <=> (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) | tptp_fun__E_(f(B_19), f(suc(B_19)))) <=> ((tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(B_19), f(suc(B_19)))))), rewrite(((tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(B_19), f(suc(B_19)))) <=> (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) | tptp_fun__E_(f(B_19), f(suc(B_19)))) <=> (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))))),
% 11.46/7.64      inference(bind,[status(th)],[])).
% 11.46/7.64  tff(108,plain,
% 11.46/7.64      (![B_18: $i, A_2: $i, B_19: $i] : (((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) | tptp_fun__E_(f(B_19), f(suc(B_19)))) <=> ![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(quant_intro,[status(thm)],[107])).
% 11.46/7.64  tff(109,axiom,(![B_18: $i, A_2: $i, B_19: $i] : (((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) | tptp_fun__E_(f(B_19), f(suc(B_19))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_20')).
% 11.46/7.64  tff(110,plain,
% 11.46/7.64      (![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(modus_ponens,[status(thm)],[109, 108])).
% 11.46/7.64  tff(111,plain,
% 11.46/7.64      (![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(modus_ponens,[status(thm)],[110, 106])).
% 11.46/7.64  tff(112,plain,(
% 11.46/7.64      ![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(skolemize,[status(sab)],[111])).
% 11.46/7.64  tff(113,plain,
% 11.46/7.64      (![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.64      inference(modus_ponens,[status(thm)],[112, 105])).
% 11.46/7.64  tff(114,plain,
% 11.46/7.64      (((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 11.46/7.64      inference(rewrite,[status(thm)],[])).
% 11.46/7.64  tff(115,plain,
% 11.46/7.64      ((tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 11.46/7.64      inference(rewrite,[status(thm)],[])).
% 11.46/7.64  tff(116,plain,
% 11.46/7.64      (((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 11.46/7.64      inference(monotonicity,[status(thm)],[115])).
% 11.46/7.64  tff(117,plain,
% 11.46/7.64      (((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 11.46/7.64      inference(transitivity,[status(thm)],[116, 114])).
% 11.46/7.64  tff(118,plain,
% 11.46/7.64      ((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 11.46/7.64      inference(quant_inst,[status(thm)],[])).
% 11.46/7.64  tff(119,plain,
% 11.46/7.64      ((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 11.46/7.64      inference(modus_ponens,[status(thm)],[118, 117])).
% 11.46/7.64  tff(120,plain,
% 11.46/7.64      ((~tptp_fun__E_(|'0'|, f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 11.46/7.64      inference(unit_resolution,[status(thm)],[119, 113])).
% 11.46/7.64  tff(121,plain,
% 11.46/7.64      ($false),
% 11.46/7.64      inference(unit_resolution,[status(thm)],[120, 103, 1, 85, 84])).
% 11.46/7.64  tff(122,plain,(tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 11.46/7.64  tff(123,plain,
% 11.46/7.64      ($false),
% 11.46/7.64      inference(unit_resolution,[status(thm)],[122, 83, 50, 1])).
% 11.46/7.64  tff(124,plain,(tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 11.46/7.64  tff(125,plain,
% 11.46/7.64      (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 11.46/7.64      inference(unit_resolution,[status(thm)],[124, 1])).
% 11.46/7.64  tff(126,assumption,(tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 11.46/7.64  tff(127,assumption,(tptp_fun__E_(s(|'0'|), f(z))), introduced(assumption)).
% 11.46/7.64  tff(128,plain,
% 11.46/7.64      (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))),
% 11.46/7.64      inference(bind,[status(th)],[])).
% 11.46/7.64  tff(129,plain,
% 11.46/7.64      (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.65      inference(quant_intro,[status(thm)],[128])).
% 11.46/7.65  tff(130,plain,
% 11.46/7.65      (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.65      inference(rewrite,[status(thm)],[])).
% 11.46/7.65  tff(131,plain,
% 11.46/7.65      (^[A_1: $i] : trans(monotonicity(rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))), (((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> ((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1))))), rewrite(((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))), (((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))))),
% 11.46/7.65      inference(bind,[status(th)],[])).
% 11.46/7.65  tff(132,plain,
% 11.46/7.65      (![A_1: $i] : ((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.65      inference(quant_intro,[status(thm)],[131])).
% 11.46/7.65  tff(133,axiom,(![A_1: $i] : ((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_85')).
% 11.46/7.65  tff(134,plain,
% 11.46/7.65      (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.65      inference(modus_ponens,[status(thm)],[133, 132])).
% 11.46/7.65  tff(135,plain,
% 11.46/7.65      (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.65      inference(modus_ponens,[status(thm)],[134, 130])).
% 11.46/7.65  tff(136,plain,(
% 11.46/7.65      ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.65      inference(skolemize,[status(sab)],[135])).
% 11.46/7.65  tff(137,plain,
% 11.46/7.65      (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.65      inference(modus_ponens,[status(thm)],[136, 129])).
% 11.46/7.65  tff(138,plain,
% 11.46/7.65      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 11.46/7.65      inference(rewrite,[status(thm)],[])).
% 11.46/7.65  tff(139,plain,
% 11.46/7.65      ((iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 11.46/7.65      inference(rewrite,[status(thm)],[])).
% 11.46/7.65  tff(140,plain,
% 11.46/7.65      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z)))))),
% 11.46/7.65      inference(monotonicity,[status(thm)],[139])).
% 11.46/7.65  tff(141,plain,
% 11.46/7.65      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 11.46/7.65      inference(transitivity,[status(thm)],[140, 138])).
% 11.46/7.65  tff(142,plain,
% 11.46/7.65      ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 11.46/7.65      inference(quant_inst,[status(thm)],[])).
% 11.46/7.65  tff(143,plain,
% 11.46/7.65      ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 11.46/7.65      inference(modus_ponens,[status(thm)],[142, 141])).
% 11.46/7.65  tff(144,plain,
% 11.46/7.65      ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 11.46/7.65      inference(unit_resolution,[status(thm)],[143, 137])).
% 11.46/7.65  tff(145,plain,
% 11.46/7.65      (iLEQ(suc(z), suc(z))),
% 11.46/7.65      inference(unit_resolution,[status(thm)],[144, 127, 1, 126])).
% 11.46/7.65  tff(146,plain,
% 11.46/7.65      (^[B_11: $i, A_1: $i, B_12: $i] : refl((tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) <=> (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))),
% 11.46/7.65      inference(bind,[status(th)],[])).
% 11.46/7.65  tff(147,plain,
% 11.46/7.65      (![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) <=> ![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 11.46/7.65      inference(quant_intro,[status(thm)],[146])).
% 11.46/7.65  tff(148,plain,
% 11.46/7.65      (![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) <=> ![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 11.46/7.65      inference(rewrite,[status(thm)],[])).
% 11.46/7.65  tff(149,plain,
% 11.46/7.65      (^[B_11: $i, A_1: $i, B_12: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) <=> (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> (((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~iLEQ(suc(B_11), suc(B_12)))))), rewrite((((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))))), rewrite((((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) <=> ((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | tptp_fun__E_(f(B_11), f(suc(B_11)))))), rewrite(((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) <=> (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) <=> (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) | tptp_fun__E_(f(B_12), f(suc(B_12)))) <=> ((tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | tptp_fun__E_(f(B_12), f(suc(B_12)))))), rewrite(((tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | tptp_fun__E_(f(B_12), f(suc(B_12)))) <=> (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) | tptp_fun__E_(f(B_12), f(suc(B_12)))) <=> (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))))),
% 11.46/7.65      inference(bind,[status(th)],[])).
% 11.46/7.65  tff(150,plain,
% 11.46/7.65      (![B_11: $i, A_1: $i, B_12: $i] : (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) | tptp_fun__E_(f(B_12), f(suc(B_12)))) <=> ![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 11.46/7.65      inference(quant_intro,[status(thm)],[149])).
% 11.46/7.65  tff(151,axiom,(![B_11: $i, A_1: $i, B_12: $i] : (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) | tptp_fun__E_(f(B_12), f(suc(B_12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_106')).
% 11.46/7.65  tff(152,plain,
% 11.46/7.65      (![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 11.46/7.65      inference(modus_ponens,[status(thm)],[151, 150])).
% 11.46/7.65  tff(153,plain,
% 11.46/7.65      (![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 11.46/7.65      inference(modus_ponens,[status(thm)],[152, 148])).
% 11.46/7.65  tff(154,plain,(
% 11.46/7.65      ![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 11.46/7.65      inference(skolemize,[status(sab)],[153])).
% 11.46/7.65  tff(155,plain,
% 11.46/7.65      (![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 11.46/7.65      inference(modus_ponens,[status(thm)],[154, 147])).
% 11.46/7.65  tff(156,plain,
% 11.46/7.65      (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 11.46/7.65      inference(rewrite,[status(thm)],[])).
% 11.46/7.65  tff(157,plain,
% 11.46/7.65      ((tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 11.46/7.65      inference(rewrite,[status(thm)],[])).
% 11.46/7.65  tff(158,plain,
% 11.46/7.65      (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 11.46/7.65      inference(monotonicity,[status(thm)],[157])).
% 11.46/7.65  tff(159,plain,
% 11.46/7.65      (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 11.46/7.65      inference(transitivity,[status(thm)],[158, 156])).
% 11.46/7.65  tff(160,plain,
% 11.46/7.65      ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 11.46/7.65      inference(quant_inst,[status(thm)],[])).
% 11.46/7.65  tff(161,plain,
% 11.46/7.65      ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 11.46/7.65      inference(modus_ponens,[status(thm)],[160, 159])).
% 11.46/7.65  tff(162,plain,
% 11.46/7.65      ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 11.46/7.65      inference(unit_resolution,[status(thm)],[161, 155])).
% 11.46/7.65  tff(163,plain,
% 11.46/7.65      ($false),
% 11.46/7.65      inference(unit_resolution,[status(thm)],[162, 145, 127, 126, 1])).
% 11.46/7.65  tff(164,plain,((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 11.46/7.65  tff(165,plain,
% 11.46/7.65      (~tptp_fun__E_(s(|'0'|), f(z))),
% 11.46/7.65      inference(unit_resolution,[status(thm)],[164, 125, 1])).
% 11.46/7.65  tff(166,plain,
% 11.46/7.65      ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 11.46/7.65      inference(quant_inst,[status(thm)],[])).
% 11.46/7.65  tff(167,plain,
% 11.46/7.65      (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 11.46/7.65      inference(unit_resolution,[status(thm)],[166, 8])).
% 11.46/7.65  tff(168,plain,
% 11.46/7.65      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 11.46/7.65      inference(rewrite,[status(thm)],[])).
% 11.46/7.65  tff(169,plain,
% 11.46/7.65      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 11.46/7.65      inference(quant_inst,[status(thm)],[])).
% 11.46/7.65  tff(170,plain,
% 11.46/7.65      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 11.46/7.65      inference(modus_ponens,[status(thm)],[169, 168])).
% 11.46/7.65  tff(171,plain,
% 11.46/7.65      (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 11.46/7.65      inference(unit_resolution,[status(thm)],[170, 60])).
% 11.46/7.65  tff(172,plain,
% 11.46/7.65      (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z))),
% 11.46/7.65      inference(unit_resolution,[status(thm)],[171, 167])).
% 11.46/7.66  tff(173,plain,
% 11.46/7.66      (tptp_fun__LE_(f(z), s(|'0'|))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[172, 165])).
% 11.46/7.66  tff(174,plain,
% 11.46/7.66      (tptp_fun__E_(|'0'|, f(z))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[49, 173])).
% 11.46/7.66  tff(175,plain,
% 11.46/7.66      (~tptp_fun__E_(|'0'|, f(suc(z)))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[122, 174, 1])).
% 11.46/7.66  tff(176,plain,
% 11.46/7.66      (~tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[82, 175])).
% 11.46/7.66  tff(177,assumption,(~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))), introduced(assumption)).
% 11.46/7.66  tff(178,plain,
% 11.46/7.66      ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))),
% 11.46/7.66      inference(quant_inst,[status(thm)],[])).
% 11.46/7.66  tff(179,plain,
% 11.46/7.66      ($false),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[178, 8, 177])).
% 11.46/7.66  tff(180,plain,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 11.46/7.66  tff(181,plain,
% 11.46/7.66      (^[B_10: $i] : refl((tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|))))))),
% 11.46/7.66      inference(bind,[status(th)],[])).
% 11.46/7.66  tff(182,plain,
% 11.46/7.66      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|))))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 11.46/7.66      inference(quant_intro,[status(thm)],[181])).
% 11.46/7.66  tff(183,plain,
% 11.46/7.66      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|))))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 11.46/7.66      inference(rewrite,[status(thm)],[])).
% 11.46/7.66  tff(184,plain,
% 11.46/7.66      (^[B_10: $i] : rewrite((((~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10))))) | tptp_fun__LE_(f(B_10), s(|'0'|))) <=> (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|))))))),
% 11.46/7.66      inference(bind,[status(th)],[])).
% 11.46/7.66  tff(185,plain,
% 11.46/7.66      (![B_10: $i] : (((~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10))))) | tptp_fun__LE_(f(B_10), s(|'0'|))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 11.46/7.66      inference(quant_intro,[status(thm)],[184])).
% 11.46/7.66  tff(186,axiom,(![B_10: $i] : (((~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10))))) | tptp_fun__LE_(f(B_10), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_33')).
% 11.46/7.66  tff(187,plain,
% 11.46/7.66      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 11.46/7.66      inference(modus_ponens,[status(thm)],[186, 185])).
% 11.46/7.66  tff(188,plain,
% 11.46/7.66      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 11.46/7.66      inference(modus_ponens,[status(thm)],[187, 183])).
% 11.46/7.66  tff(189,plain,(
% 11.46/7.66      ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 11.46/7.66      inference(skolemize,[status(sab)],[188])).
% 11.46/7.66  tff(190,plain,
% 11.46/7.66      (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 11.46/7.66      inference(modus_ponens,[status(thm)],[189, 182])).
% 11.46/7.66  tff(191,plain,
% 11.46/7.66      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))),
% 11.46/7.66      inference(rewrite,[status(thm)],[])).
% 11.46/7.66  tff(192,plain,
% 11.46/7.66      ((tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))),
% 11.46/7.66      inference(rewrite,[status(thm)],[])).
% 11.46/7.66  tff(193,plain,
% 11.46/7.66      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))),
% 11.46/7.66      inference(monotonicity,[status(thm)],[192])).
% 11.46/7.66  tff(194,plain,
% 11.46/7.66      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))),
% 11.46/7.66      inference(transitivity,[status(thm)],[193, 191])).
% 11.46/7.66  tff(195,plain,
% 11.46/7.66      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))))),
% 11.46/7.66      inference(quant_inst,[status(thm)],[])).
% 11.46/7.66  tff(196,plain,
% 11.46/7.66      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 11.46/7.66      inference(modus_ponens,[status(thm)],[195, 194])).
% 11.46/7.66  tff(197,plain,
% 11.46/7.66      (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[196, 190])).
% 11.46/7.66  tff(198,plain,
% 11.46/7.66      (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[197, 180])).
% 11.46/7.66  tff(199,plain,
% 11.46/7.66      (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[198, 176])).
% 11.46/7.66  tff(200,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), introduced(assumption)).
% 11.46/7.66  tff(201,plain,
% 11.46/7.66      ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))),
% 11.46/7.66      inference(quant_inst,[status(thm)],[])).
% 11.46/7.66  tff(202,plain,
% 11.46/7.66      ($false),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[201, 8, 200])).
% 11.46/7.66  tff(203,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 11.46/7.66  tff(204,plain,
% 11.46/7.66      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 11.46/7.66      inference(rewrite,[status(thm)],[])).
% 11.46/7.66  tff(205,plain,
% 11.46/7.66      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 11.46/7.66      inference(quant_inst,[status(thm)],[])).
% 11.46/7.66  tff(206,plain,
% 11.46/7.66      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 11.46/7.66      inference(modus_ponens,[status(thm)],[205, 204])).
% 11.46/7.66  tff(207,plain,
% 11.46/7.66      (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[206, 21])).
% 11.46/7.66  tff(208,plain,
% 11.46/7.66      (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[207, 203])).
% 11.46/7.66  tff(209,plain,
% 11.46/7.66      (tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[208, 176])).
% 11.46/7.66  tff(210,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))), introduced(assumption)).
% 11.46/7.66  tff(211,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 11.46/7.66  tff(212,assumption,(~iLEQ(suc(suc(z)), suc(suc(z)))), introduced(assumption)).
% 11.46/7.66  tff(213,plain,
% 11.46/7.66      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | iLEQ(suc(suc(z)), suc(suc(z))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 11.46/7.66      inference(rewrite,[status(thm)],[])).
% 11.46/7.66  tff(214,plain,
% 11.46/7.66      ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 11.46/7.66      inference(quant_inst,[status(thm)],[])).
% 11.46/7.66  tff(215,plain,
% 11.46/7.66      ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | iLEQ(suc(suc(z)), suc(suc(z))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 11.46/7.66      inference(modus_ponens,[status(thm)],[214, 213])).
% 11.46/7.66  tff(216,plain,
% 11.46/7.66      (iLEQ(suc(suc(z)), suc(suc(z))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[215, 137])).
% 11.46/7.66  tff(217,plain,
% 11.46/7.66      (tptp_fun__E_(f(suc(z)), f(suc(suc(z))))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[216, 212, 211, 126])).
% 11.46/7.66  tff(218,plain,
% 11.46/7.66      (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))),
% 11.46/7.66      inference(bind,[status(th)],[])).
% 11.46/7.66  tff(219,plain,
% 11.46/7.66      (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.66      inference(quant_intro,[status(thm)],[218])).
% 11.46/7.66  tff(220,plain,
% 11.46/7.66      (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.66      inference(rewrite,[status(thm)],[])).
% 11.46/7.66  tff(221,plain,
% 11.46/7.66      (^[A_1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (((~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))), rewrite((((~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (((~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1))))), rewrite((((~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))))),
% 11.46/7.66      inference(bind,[status(th)],[])).
% 11.46/7.66  tff(222,plain,
% 11.46/7.66      (![A_1: $i] : (((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.66      inference(quant_intro,[status(thm)],[221])).
% 11.46/7.66  tff(223,axiom,(![A_1: $i] : (((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_25')).
% 11.46/7.66  tff(224,plain,
% 11.46/7.66      (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.66      inference(modus_ponens,[status(thm)],[223, 222])).
% 11.46/7.66  tff(225,plain,
% 11.46/7.66      (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.66      inference(modus_ponens,[status(thm)],[224, 220])).
% 11.46/7.66  tff(226,plain,(
% 11.46/7.66      ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.66      inference(skolemize,[status(sab)],[225])).
% 11.46/7.66  tff(227,plain,
% 11.46/7.66      (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 11.46/7.66      inference(modus_ponens,[status(thm)],[226, 219])).
% 11.46/7.66  tff(228,plain,
% 11.46/7.66      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))))),
% 11.46/7.66      inference(rewrite,[status(thm)],[])).
% 11.46/7.66  tff(229,plain,
% 11.46/7.66      ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))))),
% 11.46/7.66      inference(rewrite,[status(thm)],[])).
% 11.46/7.66  tff(230,plain,
% 11.46/7.66      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z)))))))),
% 11.46/7.66      inference(monotonicity,[status(thm)],[229])).
% 11.46/7.66  tff(231,plain,
% 11.46/7.66      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))))),
% 11.46/7.66      inference(transitivity,[status(thm)],[230, 228])).
% 11.46/7.66  tff(232,plain,
% 11.46/7.66      ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 11.46/7.66      inference(quant_inst,[status(thm)],[])).
% 11.46/7.66  tff(233,plain,
% 11.46/7.66      ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z)))))),
% 11.46/7.66      inference(modus_ponens,[status(thm)],[232, 231])).
% 11.46/7.66  tff(234,plain,
% 11.46/7.66      (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z)))))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[233, 227])).
% 11.46/7.66  tff(235,plain,
% 11.46/7.66      ($false),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[234, 217, 212, 211, 126, 210])).
% 11.46/7.66  tff(236,plain,(iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.46/7.66  tff(237,plain,
% 11.46/7.66      (iLEQ(suc(suc(z)), suc(suc(z)))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[236, 199, 125, 209])).
% 11.46/7.66  tff(238,plain,
% 11.46/7.66      (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 11.46/7.66      inference(rewrite,[status(thm)],[])).
% 11.46/7.66  tff(239,plain,
% 11.46/7.66      ((tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 11.46/7.66      inference(rewrite,[status(thm)],[])).
% 11.46/7.66  tff(240,plain,
% 11.46/7.66      (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 11.46/7.66      inference(monotonicity,[status(thm)],[239])).
% 11.46/7.66  tff(241,plain,
% 11.46/7.66      (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 11.46/7.66      inference(transitivity,[status(thm)],[240, 238])).
% 11.46/7.66  tff(242,plain,
% 11.46/7.66      ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 11.46/7.66      inference(quant_inst,[status(thm)],[])).
% 11.46/7.66  tff(243,plain,
% 11.46/7.66      ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 11.46/7.66      inference(modus_ponens,[status(thm)],[242, 241])).
% 11.46/7.66  tff(244,plain,
% 11.46/7.66      (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[243, 155])).
% 11.46/7.66  tff(245,plain,
% 11.46/7.66      (tptp_fun__E_(f(suc(z)), f(suc(suc(z))))),
% 11.46/7.66      inference(unit_resolution,[status(thm)],[244, 237, 125, 209])).
% 11.46/7.66  tff(246,plain,
% 11.46/7.66      (^[B_11: $i, A_1: $i, B_12: $i] : refl(((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))),
% 11.46/7.66      inference(bind,[status(th)],[])).
% 11.46/7.66  tff(247,plain,
% 11.46/7.66      (![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> ![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 11.46/7.66      inference(quant_intro,[status(thm)],[246])).
% 11.46/7.66  tff(248,plain,
% 11.46/7.66      (![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> ![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 11.46/7.66      inference(rewrite,[status(thm)],[])).
% 11.46/7.66  tff(249,plain,
% 11.46/7.66      (^[B_11: $i, A_1: $i, B_12: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) <=> (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) <=> ((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) <=> ((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> (((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) <=> (((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))))), rewrite((((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) <=> ((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) <=> ((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) <=> (((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))))), rewrite((((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~iLEQ(suc(A_1), suc(B_11)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> (((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~iLEQ(suc(B_11), suc(B_12)))))), rewrite((((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))))),
% 11.46/7.67      inference(bind,[status(th)],[])).
% 11.46/7.67  tff(250,plain,
% 11.46/7.67      (![B_11: $i, A_1: $i, B_12: $i] : ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 11.46/7.67      inference(quant_intro,[status(thm)],[249])).
% 11.46/7.67  tff(251,axiom,(![B_11: $i, A_1: $i, B_12: $i] : ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_8')).
% 11.46/7.67  tff(252,plain,
% 11.46/7.67      (![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 11.46/7.67      inference(modus_ponens,[status(thm)],[251, 250])).
% 11.46/7.67  tff(253,plain,
% 11.46/7.67      (![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 11.46/7.67      inference(modus_ponens,[status(thm)],[252, 248])).
% 11.46/7.67  tff(254,plain,(
% 11.46/7.67      ![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 11.46/7.67      inference(skolemize,[status(sab)],[253])).
% 11.46/7.67  tff(255,plain,
% 11.46/7.67      (![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 11.46/7.67      inference(modus_ponens,[status(thm)],[254, 247])).
% 11.46/7.67  tff(256,plain,
% 11.46/7.67      (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 11.46/7.67      inference(rewrite,[status(thm)],[])).
% 11.46/7.67  tff(257,plain,
% 11.46/7.67      (((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 11.46/7.67      inference(rewrite,[status(thm)],[])).
% 11.46/7.67  tff(258,plain,
% 11.46/7.67      (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 11.46/7.67      inference(monotonicity,[status(thm)],[257])).
% 11.46/7.67  tff(259,plain,
% 11.46/7.67      (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 11.46/7.67      inference(transitivity,[status(thm)],[258, 256])).
% 11.46/7.67  tff(260,plain,
% 11.46/7.67      ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))),
% 11.46/7.67      inference(quant_inst,[status(thm)],[])).
% 11.46/7.67  tff(261,plain,
% 11.46/7.67      ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 11.46/7.68      inference(modus_ponens,[status(thm)],[260, 259])).
% 11.46/7.68  tff(262,plain,
% 11.46/7.68      ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[261, 255])).
% 11.46/7.68  tff(263,plain,
% 11.46/7.68      ($false),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[262, 245, 237, 209, 125, 199])).
% 11.46/7.68  tff(264,plain,(tptp_fun__E_(f(z), f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 11.46/7.68  tff(265,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))), introduced(assumption)).
% 11.46/7.68  tff(266,assumption,(~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))), introduced(assumption)).
% 11.46/7.68  tff(267,plain,
% 11.46/7.68      ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))),
% 11.46/7.68      inference(quant_inst,[status(thm)],[])).
% 11.46/7.68  tff(268,plain,
% 11.46/7.68      ($false),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[267, 8, 266])).
% 11.46/7.68  tff(269,plain,(tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 11.46/7.68  tff(270,plain,
% 11.46/7.68      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))))),
% 11.46/7.68      inference(rewrite,[status(thm)],[])).
% 11.46/7.68  tff(271,plain,
% 11.46/7.68      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))))),
% 11.46/7.68      inference(quant_inst,[status(thm)],[])).
% 11.46/7.68  tff(272,plain,
% 11.46/7.68      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|))))),
% 11.46/7.68      inference(modus_ponens,[status(thm)],[271, 270])).
% 11.46/7.68  tff(273,plain,
% 11.46/7.68      (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[272, 190, 269])).
% 11.46/7.68  tff(274,plain,
% 11.46/7.68      (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[273, 265])).
% 11.46/7.68  tff(275,plain,
% 11.46/7.68      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 11.46/7.68      inference(rewrite,[status(thm)],[])).
% 11.46/7.68  tff(276,plain,
% 11.46/7.68      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 11.46/7.68      inference(quant_inst,[status(thm)],[])).
% 11.46/7.68  tff(277,plain,
% 11.46/7.68      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 11.46/7.68      inference(modus_ponens,[status(thm)],[276, 275])).
% 11.46/7.68  tff(278,plain,
% 11.46/7.68      (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[277, 60, 203])).
% 11.46/7.68  tff(279,plain,
% 11.46/7.68      (tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[278, 265])).
% 11.46/7.68  tff(280,plain,
% 11.46/7.68      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))),
% 11.46/7.68      inference(rewrite,[status(thm)],[])).
% 11.46/7.68  tff(281,plain,
% 11.46/7.68      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))),
% 11.46/7.68      inference(quant_inst,[status(thm)],[])).
% 11.46/7.68  tff(282,plain,
% 11.46/7.68      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 11.46/7.68      inference(modus_ponens,[status(thm)],[281, 280])).
% 11.46/7.68  tff(283,plain,
% 11.46/7.68      (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[282, 21])).
% 11.46/7.68  tff(284,plain,
% 11.46/7.68      (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[283, 180])).
% 11.46/7.68  tff(285,plain,
% 11.46/7.68      (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[284, 265])).
% 11.46/7.68  tff(286,assumption,(~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))), introduced(assumption)).
% 11.46/7.68  tff(287,plain,
% 11.46/7.68      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))))),
% 11.46/7.68      inference(rewrite,[status(thm)],[])).
% 11.46/7.68  tff(288,plain,
% 11.46/7.68      ((iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))))),
% 11.46/7.68      inference(rewrite,[status(thm)],[])).
% 11.46/7.68  tff(289,plain,
% 11.46/7.68      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))))),
% 11.46/7.68      inference(monotonicity,[status(thm)],[288])).
% 11.46/7.68  tff(290,plain,
% 11.46/7.68      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))))),
% 11.46/7.68      inference(transitivity,[status(thm)],[289, 287])).
% 11.46/7.68  tff(291,plain,
% 11.46/7.68      ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 11.46/7.68      inference(quant_inst,[status(thm)],[])).
% 11.46/7.68  tff(292,plain,
% 11.46/7.68      ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))),
% 11.46/7.68      inference(modus_ponens,[status(thm)],[291, 290])).
% 11.46/7.68  tff(293,plain,
% 11.46/7.68      ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[292, 137])).
% 11.46/7.68  tff(294,plain,
% 11.46/7.68      (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[293, 286, 211, 210])).
% 11.46/7.68  tff(295,plain,
% 11.46/7.68      (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 11.46/7.68      inference(rewrite,[status(thm)],[])).
% 11.46/7.68  tff(296,plain,
% 11.46/7.68      ((tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 11.46/7.68      inference(rewrite,[status(thm)],[])).
% 11.46/7.68  tff(297,plain,
% 11.46/7.68      (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))))),
% 11.46/7.68      inference(monotonicity,[status(thm)],[296])).
% 11.46/7.68  tff(298,plain,
% 11.46/7.68      (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 11.46/7.68      inference(transitivity,[status(thm)],[297, 295])).
% 11.46/7.68  tff(299,plain,
% 11.46/7.68      ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))),
% 11.46/7.68      inference(quant_inst,[status(thm)],[])).
% 11.46/7.68  tff(300,plain,
% 11.46/7.68      ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 11.46/7.68      inference(modus_ponens,[status(thm)],[299, 298])).
% 11.46/7.68  tff(301,plain,
% 11.46/7.68      ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[300, 155])).
% 11.46/7.68  tff(302,plain,
% 11.46/7.68      ($false),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[301, 294, 286, 211, 210])).
% 11.46/7.68  tff(303,plain,(tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))), inference(lemma,lemma(discharge,[]))).
% 11.46/7.68  tff(304,plain,
% 11.46/7.68      (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[303, 279, 285])).
% 11.46/7.68  tff(305,plain,
% 11.46/7.68      (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 11.46/7.68      inference(rewrite,[status(thm)],[])).
% 11.46/7.68  tff(306,plain,
% 11.46/7.68      (((~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 11.46/7.68      inference(rewrite,[status(thm)],[])).
% 11.46/7.68  tff(307,plain,
% 11.46/7.68      (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))))),
% 11.46/7.68      inference(monotonicity,[status(thm)],[306])).
% 11.46/7.68  tff(308,plain,
% 11.46/7.68      (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 11.46/7.68      inference(transitivity,[status(thm)],[307, 305])).
% 11.46/7.68  tff(309,plain,
% 11.46/7.68      ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))))),
% 11.46/7.68      inference(quant_inst,[status(thm)],[])).
% 11.46/7.68  tff(310,plain,
% 11.46/7.68      ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 11.46/7.68      inference(modus_ponens,[status(thm)],[309, 308])).
% 11.46/7.68  tff(311,plain,
% 11.46/7.68      ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[310, 255])).
% 11.46/7.68  tff(312,plain,
% 11.46/7.68      (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 11.46/7.68      inference(unit_resolution,[status(thm)],[311, 304, 279, 274, 285])).
% 11.46/7.68  tff(313,plain,
% 11.46/7.68      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 11.46/7.68      inference(rewrite,[status(thm)],[])).
% 11.46/7.68  tff(314,plain,
% 11.46/7.68      ((iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 11.46/7.68      inference(rewrite,[status(thm)],[])).
% 11.46/7.68  tff(315,plain,
% 11.46/7.68      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 11.46/7.68      inference(monotonicity,[status(thm)],[314])).
% 11.46/7.68  tff(316,plain,
% 11.46/7.68      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 11.46/7.68      inference(transitivity,[status(thm)],[315, 313])).
% 11.46/7.68  tff(317,plain,
% 11.46/7.68      ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 11.46/7.68      inference(quant_inst,[status(thm)],[])).
% 11.46/7.68  tff(318,plain,
% 11.46/7.68      ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 11.46/7.69      inference(modus_ponens,[status(thm)],[317, 316])).
% 11.46/7.69  tff(319,plain,
% 11.46/7.69      ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[318, 227])).
% 11.46/7.69  tff(320,plain,
% 11.46/7.69      ($false),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[319, 312, 304, 285, 279, 274])).
% 11.46/7.69  tff(321,plain,(tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 11.46/7.69  tff(322,plain,
% 11.46/7.69      (^[B_17: $i] : refl((tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|)))) <=> (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|)))))),
% 11.46/7.69      inference(bind,[status(th)],[])).
% 11.46/7.69  tff(323,plain,
% 11.46/7.69      (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|)))) <=> ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 11.46/7.69      inference(quant_intro,[status(thm)],[322])).
% 11.46/7.69  tff(324,plain,
% 11.46/7.69      (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|)))) <=> ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 11.46/7.69      inference(rewrite,[status(thm)],[])).
% 11.46/7.69  tff(325,plain,
% 11.46/7.69      (^[B_17: $i] : rewrite((((~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_17))))) | tptp_fun__LE_(f(B_17), |'0'|)) <=> (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|)))))),
% 11.46/7.69      inference(bind,[status(th)],[])).
% 11.46/7.69  tff(326,plain,
% 11.46/7.69      (![B_17: $i] : (((~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_17))))) | tptp_fun__LE_(f(B_17), |'0'|)) <=> ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 11.46/7.69      inference(quant_intro,[status(thm)],[325])).
% 11.46/7.69  tff(327,axiom,(![B_17: $i] : (((~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_17))))) | tptp_fun__LE_(f(B_17), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_51')).
% 11.46/7.69  tff(328,plain,
% 11.46/7.69      (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 11.46/7.69      inference(modus_ponens,[status(thm)],[327, 326])).
% 11.46/7.69  tff(329,plain,
% 11.46/7.69      (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 11.46/7.69      inference(modus_ponens,[status(thm)],[328, 324])).
% 11.46/7.69  tff(330,plain,(
% 11.46/7.69      ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 11.46/7.69      inference(skolemize,[status(sab)],[329])).
% 11.46/7.69  tff(331,plain,
% 11.46/7.69      (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 11.46/7.69      inference(modus_ponens,[status(thm)],[330, 323])).
% 11.46/7.69  tff(332,plain,
% 11.46/7.69      (((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))))) <=> ((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))))),
% 11.46/7.69      inference(rewrite,[status(thm)],[])).
% 11.46/7.69  tff(333,plain,
% 11.46/7.69      ((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))))),
% 11.46/7.69      inference(quant_inst,[status(thm)],[])).
% 11.46/7.69  tff(334,plain,
% 11.46/7.69      ((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))),
% 11.46/7.69      inference(modus_ponens,[status(thm)],[333, 332])).
% 11.46/7.69  tff(335,plain,
% 11.46/7.69      (tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[334, 42, 331])).
% 11.46/7.69  tff(336,plain,
% 11.46/7.69      (tptp_fun__E_(|'0'|, f(suc(suc(z))))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[335, 321])).
% 11.46/7.69  tff(337,assumption,(~tptp_fun__LE_(f(suc(z)), s(|'0'|))), introduced(assumption)).
% 11.46/7.69  tff(338,plain,
% 11.46/7.69      (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[198, 337])).
% 11.46/7.69  tff(339,plain,
% 11.46/7.69      (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[67, 10])).
% 11.46/7.69  tff(340,plain,
% 11.46/7.69      (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[339, 337])).
% 11.46/7.69  tff(341,plain,
% 11.46/7.69      (tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[208, 337])).
% 11.46/7.69  tff(342,plain,
% 11.46/7.69      (iLEQ(suc(suc(z)), suc(suc(z)))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[236, 340, 338, 341])).
% 11.46/7.69  tff(343,plain,
% 11.46/7.69      (tptp_fun__E_(f(suc(z)), f(suc(suc(z))))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[244, 340, 342, 341])).
% 11.46/7.69  tff(344,plain,
% 11.46/7.69      ($false),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[262, 343, 342, 341, 340, 338])).
% 11.46/7.69  tff(345,plain,(tptp_fun__LE_(f(suc(z)), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 11.46/7.69  tff(346,plain,
% 11.46/7.69      (tptp_fun__E_(|'0'|, f(suc(z)))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[82, 345])).
% 11.46/7.69  tff(347,plain,
% 11.46/7.69      (^[A_2: $i] : refl((iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))),
% 11.46/7.69      inference(bind,[status(th)],[])).
% 11.46/7.69  tff(348,plain,
% 11.46/7.69      (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.69      inference(quant_intro,[status(thm)],[347])).
% 11.46/7.69  tff(349,plain,
% 11.46/7.69      (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.69      inference(rewrite,[status(thm)],[])).
% 11.46/7.69  tff(350,plain,
% 11.46/7.69      (^[A_2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> ((~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> ((~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> (((~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))))), rewrite((((~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> (((~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))))), rewrite((((~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))))),
% 11.46/7.69      inference(bind,[status(th)],[])).
% 11.46/7.69  tff(351,plain,
% 11.46/7.69      (![A_2: $i] : (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.69      inference(quant_intro,[status(thm)],[350])).
% 11.46/7.69  tff(352,axiom,(![A_2: $i] : (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | iLEQ(suc(A_2), suc(A_2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_148')).
% 11.46/7.69  tff(353,plain,
% 11.46/7.69      (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.69      inference(modus_ponens,[status(thm)],[352, 351])).
% 11.46/7.69  tff(354,plain,
% 11.46/7.69      (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.69      inference(modus_ponens,[status(thm)],[353, 349])).
% 11.46/7.69  tff(355,plain,(
% 11.46/7.69      ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.69      inference(skolemize,[status(sab)],[354])).
% 11.46/7.69  tff(356,plain,
% 11.46/7.69      (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 11.46/7.69      inference(modus_ponens,[status(thm)],[355, 348])).
% 11.46/7.69  tff(357,plain,
% 11.46/7.69      (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 11.46/7.69      inference(rewrite,[status(thm)],[])).
% 11.46/7.69  tff(358,plain,
% 11.46/7.69      ((iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 11.46/7.69      inference(rewrite,[status(thm)],[])).
% 11.46/7.69  tff(359,plain,
% 11.46/7.69      (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))))),
% 11.46/7.69      inference(monotonicity,[status(thm)],[358])).
% 11.46/7.69  tff(360,plain,
% 11.46/7.69      (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 11.46/7.69      inference(transitivity,[status(thm)],[359, 357])).
% 11.46/7.69  tff(361,plain,
% 11.46/7.69      ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 11.46/7.69      inference(quant_inst,[status(thm)],[])).
% 11.46/7.69  tff(362,plain,
% 11.46/7.69      ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 11.46/7.69      inference(modus_ponens,[status(thm)],[361, 360])).
% 11.46/7.69  tff(363,plain,
% 11.46/7.69      ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[362, 356])).
% 11.46/7.69  tff(364,plain,
% 11.46/7.69      ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z)))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[363, 264])).
% 11.46/7.69  tff(365,plain,
% 11.46/7.69      (iLEQ(suc(z), suc(z))),
% 11.46/7.69      inference(unit_resolution,[status(thm)],[364, 85, 346, 336])).
% 11.46/7.69  tff(366,plain,
% 11.46/7.69      (^[B_18: $i, A_2: $i, B_19: $i] : refl(((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))),
% 11.46/7.69      inference(bind,[status(th)],[])).
% 11.46/7.69  tff(367,plain,
% 11.46/7.69      (![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) <=> ![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 11.46/7.69      inference(quant_intro,[status(thm)],[366])).
% 11.46/7.69  tff(368,plain,
% 11.46/7.69      (![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) <=> ![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 11.46/7.69      inference(rewrite,[status(thm)],[])).
% 11.46/7.69  tff(369,plain,
% 11.46/7.69      (^[B_18: $i, A_2: $i, B_19: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), (((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), (((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~iLEQ(suc(B_18), suc(B_19)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~iLEQ(suc(B_18), suc(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(B_19)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(B_18)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) | (~iLEQ(suc(A_2), suc(B_18)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~iLEQ(suc(A_2), suc(B_18)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~iLEQ(suc(A_2), suc(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) | (~iLEQ(suc(A_2), suc(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) | (~iLEQ(suc(A_2), suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) | (~iLEQ(suc(A_2), suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))))),
% 11.46/7.70      inference(bind,[status(th)],[])).
% 11.46/7.70  tff(370,plain,
% 11.46/7.70      (![B_18: $i, A_2: $i, B_19: $i] : ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) | (~iLEQ(suc(A_2), suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> ![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 11.46/7.70      inference(quant_intro,[status(thm)],[369])).
% 11.46/7.70  tff(371,axiom,(![B_18: $i, A_2: $i, B_19: $i] : ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) | (~iLEQ(suc(A_2), suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_204')).
% 11.46/7.70  tff(372,plain,
% 11.46/7.70      (![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 11.46/7.70      inference(modus_ponens,[status(thm)],[371, 370])).
% 11.46/7.70  tff(373,plain,
% 11.46/7.70      (![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 11.46/7.70      inference(modus_ponens,[status(thm)],[372, 368])).
% 11.46/7.70  tff(374,plain,(
% 11.46/7.70      ![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 11.46/7.70      inference(skolemize,[status(sab)],[373])).
% 11.46/7.70  tff(375,plain,
% 11.46/7.70      (![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 11.46/7.70      inference(modus_ponens,[status(thm)],[374, 367])).
% 11.46/7.70  tff(376,plain,
% 11.46/7.70      (((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 11.46/7.70      inference(rewrite,[status(thm)],[])).
% 11.46/7.70  tff(377,plain,
% 11.46/7.70      (((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 11.46/7.70      inference(rewrite,[status(thm)],[])).
% 11.46/7.70  tff(378,plain,
% 11.46/7.70      (((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | ((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))) <=> ((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 11.46/7.70      inference(monotonicity,[status(thm)],[377])).
% 11.46/7.70  tff(379,plain,
% 11.46/7.70      (((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | ((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))) <=> ((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 11.46/7.70      inference(transitivity,[status(thm)],[378, 376])).
% 11.46/7.70  tff(380,plain,
% 11.46/7.70      ((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | ((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))),
% 11.46/7.70      inference(quant_inst,[status(thm)],[])).
% 11.46/7.70  tff(381,plain,
% 11.46/7.70      ((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 11.46/7.70      inference(modus_ponens,[status(thm)],[380, 379])).
% 11.46/7.70  tff(382,plain,
% 11.46/7.70      ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 11.46/7.70      inference(unit_resolution,[status(thm)],[381, 375, 264])).
% 11.46/7.70  tff(383,plain,
% 11.46/7.70      ($false),
% 11.46/7.70      inference(unit_resolution,[status(thm)],[382, 365, 85, 346, 336])).
% 11.46/7.70  tff(384,plain,(~tptp_fun__E_(|'0'|, f(z))), inference(lemma,lemma(discharge,[]))).
% 11.46/7.70  tff(385,plain,
% 11.46/7.70      (~tptp_fun__LE_(f(z), s(|'0'|))),
% 11.46/7.70      inference(unit_resolution,[status(thm)],[49, 384])).
% 11.46/7.70  tff(386,plain,
% 11.46/7.70      (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 11.46/7.70      inference(unit_resolution,[status(thm)],[28, 10])).
% 11.46/7.70  tff(387,plain,
% 11.46/7.70      (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 11.46/7.70      inference(unit_resolution,[status(thm)],[386, 385])).
% 11.46/7.70  tff(388,plain,
% 11.46/7.70      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 11.46/7.70      inference(rewrite,[status(thm)],[])).
% 11.46/7.70  tff(389,plain,
% 11.46/7.70      ((tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 11.46/7.70      inference(rewrite,[status(thm)],[])).
% 11.46/7.70  tff(390,plain,
% 11.46/7.70      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 11.46/7.70      inference(monotonicity,[status(thm)],[389])).
% 11.46/7.70  tff(391,plain,
% 11.46/7.70      (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 11.46/7.70      inference(transitivity,[status(thm)],[390, 388])).
% 11.46/7.70  tff(392,plain,
% 11.46/7.70      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 11.46/7.70      inference(quant_inst,[status(thm)],[])).
% 11.46/7.70  tff(393,plain,
% 11.46/7.70      ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 11.46/7.70      inference(modus_ponens,[status(thm)],[392, 391])).
% 11.46/7.70  tff(394,plain,
% 11.46/7.70      (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 11.46/7.70      inference(unit_resolution,[status(thm)],[393, 190])).
% 11.46/7.70  tff(395,plain,
% 11.46/7.70      (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 11.46/7.70      inference(unit_resolution,[status(thm)],[394, 203])).
% 11.46/7.70  tff(396,plain,
% 11.46/7.70      (tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 11.46/7.70      inference(unit_resolution,[status(thm)],[395, 385])).
% 11.46/7.70  tff(397,plain,
% 11.46/7.70      (tptp_fun__E_(s(|'0'|), f(z))),
% 11.46/7.70      inference(unit_resolution,[status(thm)],[172, 385])).
% 11.46/7.70  tff(398,plain,
% 11.46/7.70      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 11.46/7.70      inference(rewrite,[status(thm)],[])).
% 11.46/7.70  tff(399,plain,
% 11.46/7.70      ((iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 11.46/7.70      inference(rewrite,[status(thm)],[])).
% 11.46/7.70  tff(400,plain,
% 11.46/7.70      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))))),
% 11.46/7.70      inference(monotonicity,[status(thm)],[399])).
% 11.46/7.70  tff(401,plain,
% 11.46/7.70      (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 11.46/7.70      inference(transitivity,[status(thm)],[400, 398])).
% 11.46/7.70  tff(402,plain,
% 11.46/7.70      ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 11.46/7.70      inference(quant_inst,[status(thm)],[])).
% 11.46/7.70  tff(403,plain,
% 11.46/7.70      ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 11.46/7.70      inference(modus_ponens,[status(thm)],[402, 401])).
% 11.46/7.70  tff(404,plain,
% 11.46/7.70      ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 11.46/7.70      inference(unit_resolution,[status(thm)],[403, 227])).
% 11.46/7.70  tff(405,plain,
% 11.46/7.70      ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 11.46/7.70      inference(unit_resolution,[status(thm)],[404, 264])).
% 11.46/7.70  tff(406,plain,
% 11.46/7.70      (iLEQ(suc(z), suc(z))),
% 11.46/7.70      inference(unit_resolution,[status(thm)],[405, 397, 396, 387])).
% 11.46/7.70  tff(407,plain,
% 11.46/7.70      (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 11.46/7.70      inference(rewrite,[status(thm)],[])).
% 11.46/7.70  tff(408,plain,
% 11.46/7.70      (((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 11.46/7.70      inference(rewrite,[status(thm)],[])).
% 11.46/7.70  tff(409,plain,
% 11.46/7.70      (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 11.46/7.70      inference(monotonicity,[status(thm)],[408])).
% 11.46/7.70  tff(410,plain,
% 11.46/7.70      (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 11.46/7.70      inference(transitivity,[status(thm)],[409, 407])).
% 11.46/7.70  tff(411,plain,
% 11.46/7.70      ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 11.46/7.70      inference(quant_inst,[status(thm)],[])).
% 11.46/7.70  tff(412,plain,
% 11.46/7.70      ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 11.46/7.71      inference(modus_ponens,[status(thm)],[411, 410])).
% 11.46/7.71  tff(413,plain,
% 11.46/7.71      ($false),
% 11.46/7.71      inference(unit_resolution,[status(thm)],[412, 255, 397, 396, 387, 406, 264])).
% 11.46/7.71  % SZS output end Proof
%------------------------------------------------------------------------------