TSTP Solution File: SYO652-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO652-1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 01:41:11 EDT 2022
% Result : Unsatisfiable 0.21s 0.54s
% Output : Proof 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYO652-1 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Sep 5 15:43:17 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.54 % SZS status Unsatisfiable
% 0.21/0.54 % SZS output start Proof
% 0.21/0.54 tff(tptp_fun__E__type, type, (
% 0.21/0.54 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.21/0.54 tff(f_type, type, (
% 0.21/0.54 f: $i > $i)).
% 0.21/0.54 tff(suc_type, type, (
% 0.21/0.54 suc: $i > $i)).
% 0.21/0.54 tff(z_type, type, (
% 0.21/0.54 z: $i)).
% 0.21/0.54 tff(iLEQ_type, type, (
% 0.21/0.54 iLEQ: ( $i * $i ) > $o)).
% 0.21/0.54 tff(tptp_fun__0__type, type, (
% 0.21/0.54 tptp_fun__0_: $i)).
% 0.21/0.54 tff(tptp_fun__LE__type, type, (
% 0.21/0.54 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.21/0.54 tff(s_type, type, (
% 0.21/0.54 s: $i > $i)).
% 0.21/0.54 tff(1,assumption,(~iLEQ(suc(z), suc(z))), introduced(assumption)).
% 0.21/0.54 tff(2,assumption,(~tptp_fun__LE_(f(suc(z)), s(|'0'|))), introduced(assumption)).
% 0.21/0.54 tff(3,plain,
% 0.21/0.54 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(|'0'|)) <=> tptp_fun__LE_(f(A), s(|'0'|)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(4,plain,
% 0.21/0.54 (![A: $i] : tptp_fun__LE_(f(A), s(|'0'|)) <=> ![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.54 tff(5,plain,
% 0.21/0.54 (![A: $i] : tptp_fun__LE_(f(A), s(|'0'|)) <=> ![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(6,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_199')).
% 0.21/0.54 tff(7,plain,
% 0.21/0.54 (![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.54 tff(8,plain,(
% 0.21/0.54 ![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))),
% 0.21/0.54 inference(skolemize,[status(sab)],[7])).
% 0.21/0.54 tff(9,plain,
% 0.21/0.54 (![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.54 tff(10,plain,
% 0.21/0.54 ((~![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(11,plain,
% 0.21/0.54 ($false),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.21/0.54 tff(12,plain,(tptp_fun__LE_(f(suc(z)), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.54 tff(13,plain,
% 0.21/0.54 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(14,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_99')).
% 0.21/0.54 tff(15,plain,
% 0.21/0.54 (~tptp_fun__LE_(f(z), |'0'|)),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.21/0.54 tff(16,plain,
% 0.21/0.54 (^[B_10: $i] : refl((tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))) <=> (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(17,plain,
% 0.21/0.54 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.54 tff(18,plain,
% 0.21/0.54 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(19,plain,
% 0.21/0.54 (^[B_10: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))) | tptp_fun__LE_(f(B_10), |'0'|)) <=> (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(20,plain,
% 0.21/0.54 (![B_10: $i] : (((~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))) | tptp_fun__LE_(f(B_10), |'0'|)) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.54 tff(21,axiom,(![B_10: $i] : (((~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))) | tptp_fun__LE_(f(B_10), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_191')).
% 0.21/0.54 tff(22,plain,
% 0.21/0.54 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.55 tff(23,plain,
% 0.21/0.55 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.55 tff(24,plain,(
% 0.21/0.55 ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.21/0.55 inference(skolemize,[status(sab)],[23])).
% 0.21/0.55 tff(25,plain,
% 0.21/0.55 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.21/0.55 tff(26,plain,
% 0.21/0.55 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(27,plain,
% 0.21/0.55 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(28,plain,
% 0.21/0.55 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.55 tff(29,plain,
% 0.21/0.55 ((~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[28, 25, 15])).
% 0.21/0.55 tff(30,plain,
% 0.21/0.55 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[29, 12])).
% 0.21/0.55 tff(31,plain,
% 0.21/0.55 ((~![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))) | tptp_fun__LE_(f(z), s(|'0'|))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(32,plain,
% 0.21/0.55 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[31, 9])).
% 0.21/0.55 tff(33,plain,
% 0.21/0.55 (^[B_10: $i] : refl(((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10))) <=> ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(34,plain,
% 0.21/0.55 (![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10))) <=> ![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[33])).
% 0.21/0.55 tff(35,plain,
% 0.21/0.55 (![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10))) <=> ![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(36,plain,
% 0.21/0.55 (^[B_10: $i] : rewrite((((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_10))) | tptp_fun__LE_(f(B_10), |'0'|)) <=> ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(37,plain,
% 0.21/0.55 (![B_10: $i] : (((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_10))) | tptp_fun__LE_(f(B_10), |'0'|)) <=> ![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.55 tff(38,axiom,(![B_10: $i] : (((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_10))) | tptp_fun__LE_(f(B_10), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_17')).
% 0.21/0.55 tff(39,plain,
% 0.21/0.55 (![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.21/0.55 tff(40,plain,
% 0.21/0.55 (![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.21/0.55 tff(41,plain,(
% 0.21/0.55 ![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.21/0.55 inference(skolemize,[status(sab)],[40])).
% 0.21/0.55 tff(42,plain,
% 0.21/0.55 (![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.21/0.55 tff(43,plain,
% 0.21/0.55 (((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(44,plain,
% 0.21/0.55 (((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z))) <=> (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(45,plain,
% 0.21/0.55 (((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[44])).
% 0.21/0.55 tff(46,plain,
% 0.21/0.55 (((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.21/0.55 inference(transitivity,[status(thm)],[45, 43])).
% 0.21/0.55 tff(47,plain,
% 0.21/0.55 ((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(48,plain,
% 0.21/0.55 ((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.55 tff(49,plain,
% 0.21/0.55 (tptp_fun__E_(|'0'|, f(z))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[48, 42, 15, 32])).
% 0.21/0.55 tff(50,plain,
% 0.21/0.55 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(51,plain,
% 0.21/0.55 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.55 tff(52,plain,
% 0.21/0.55 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(53,plain,
% 0.21/0.55 (^[A_1: $i] : trans(monotonicity(rewrite((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))), (((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'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_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))), (((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'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_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))))),
% 0.21/0.55 inference(bind,[status(th)],[])).
% 0.21/0.55 tff(54,plain,
% 0.21/0.55 (![A_1: $i] : ((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'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_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[53])).
% 0.21/0.55 tff(55,axiom,(![A_1: $i] : ((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'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/sandbox/benchmark/theBenchmark.p','clause_44')).
% 0.21/0.55 tff(56,plain,
% 0.21/0.55 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.21/0.55 tff(57,plain,
% 0.21/0.55 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.21/0.55 tff(58,plain,(
% 0.21/0.55 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.55 inference(skolemize,[status(sab)],[57])).
% 0.21/0.55 tff(59,plain,
% 0.21/0.55 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.21/0.55 tff(60,plain,
% 0.21/0.55 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(61,plain,
% 0.21/0.55 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(62,plain,
% 0.21/0.55 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.55 tff(63,plain,
% 0.21/0.55 (iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[62, 59, 49, 30])).
% 0.21/0.56 tff(64,plain,
% 0.21/0.56 (tptp_fun__E_(f(z), f(suc(z)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[63, 1])).
% 0.21/0.56 tff(65,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))), introduced(assumption)).
% 0.21/0.56 tff(66,plain,
% 0.21/0.56 ((~![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(67,plain,
% 0.21/0.56 ($false),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[66, 9, 65])).
% 0.21/0.56 tff(68,plain,(tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.56 tff(69,plain,
% 0.21/0.56 (^[B_10: $i] : refl((tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|)))) <=> (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|)))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(70,plain,
% 0.21/0.56 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|)))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.56 tff(71,plain,
% 0.21/0.56 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|)))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(72,plain,
% 0.21/0.56 (^[B_10: $i] : rewrite((((~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_10))))) | tptp_fun__LE_(f(B_10), |'0'|)) <=> (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|)))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(73,plain,
% 0.21/0.56 (![B_10: $i] : (((~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_10))))) | tptp_fun__LE_(f(B_10), |'0'|)) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.56 tff(74,axiom,(![B_10: $i] : (((~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_10))))) | tptp_fun__LE_(f(B_10), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.21/0.56 tff(75,plain,
% 0.21/0.56 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.56 tff(76,plain,
% 0.21/0.56 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.21/0.56 tff(77,plain,(
% 0.21/0.56 ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.21/0.56 inference(skolemize,[status(sab)],[76])).
% 0.21/0.56 tff(78,plain,
% 0.21/0.56 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.21/0.56 tff(79,plain,
% 0.21/0.56 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), 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_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), 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'|))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(80,plain,
% 0.21/0.56 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), 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'|))))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(81,plain,
% 0.21/0.56 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), 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'|)))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.56 tff(82,plain,
% 0.21/0.56 (tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[81, 78, 15])).
% 0.21/0.56 tff(83,plain,
% 0.21/0.56 (tptp_fun__E_(|'0'|, f(suc(suc(z))))),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[82, 68])).
% 0.21/0.56 tff(84,plain,
% 0.21/0.56 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(85,plain,
% 0.21/0.56 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.56 tff(86,plain,
% 0.21/0.56 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(87,plain,
% 0.21/0.56 (^[A_1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))), ((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))), ((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))))), (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))), (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))), ((((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(88,plain,
% 0.21/0.56 (![A_1: $i] : (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[87])).
% 0.21/0.56 tff(89,axiom,(![A_1: $i] : (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_149')).
% 0.21/0.56 tff(90,plain,
% 0.21/0.56 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.56 tff(91,plain,
% 0.21/0.56 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.21/0.56 tff(92,plain,(
% 0.21/0.56 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.56 inference(skolemize,[status(sab)],[91])).
% 0.21/0.56 tff(93,plain,
% 0.21/0.56 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.21/0.56 tff(94,plain,
% 0.21/0.56 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(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_(f(z), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | iLEQ(suc(z), suc(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_(f(z), f(suc(z)))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(95,plain,
% 0.21/0.56 ((iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z))))) <=> (iLEQ(suc(z), suc(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_(f(z), f(suc(z)))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(96,plain,
% 0.21/0.57 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(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_(f(z), f(suc(z))))))),
% 0.21/0.57 inference(monotonicity,[status(thm)],[95])).
% 0.21/0.57 tff(97,plain,
% 0.21/0.57 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | iLEQ(suc(z), suc(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_(f(z), f(suc(z)))))),
% 0.21/0.57 inference(transitivity,[status(thm)],[96, 94])).
% 0.21/0.57 tff(98,plain,
% 0.21/0.57 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(99,plain,
% 0.21/0.57 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z))))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.57 tff(100,plain,
% 0.21/0.57 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z))))),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[99, 93, 49, 30, 83])).
% 0.21/0.57 tff(101,plain,
% 0.21/0.57 ($false),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[100, 64, 1])).
% 0.21/0.57 tff(102,plain,(iLEQ(suc(z), suc(z))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.57 tff(103,plain,
% 0.21/0.57 (^[B_11: $i, B_13: $i, A_1: $i, B_12: $i] : refl(((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(104,plain,
% 0.21/0.57 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) <=> ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[103])).
% 0.21/0.57 tff(105,plain,
% 0.21/0.57 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) <=> ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(106,plain,
% 0.21/0.57 (^[B_11: $i, B_13: $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(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) <=> ((~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) <=> (((~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))))), rewrite((((~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) <=> ((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) <=> ((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> (((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(A_1)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) <=> (((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_13)))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_13)))) <=> ((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) <=> ((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) <=> (((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'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_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(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_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) <=> (((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))))), rewrite((((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(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_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(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_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(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_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> (((~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~iLEQ(suc(A_1), suc(B_11)))))), rewrite((((~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~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_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) <=> (((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))))), rewrite((((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_12)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) <=> ((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) <=> ((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) <=> (((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) <=> ((~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) <=> ((~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> (((~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~iLEQ(suc(B_11), suc(B_12)))))), rewrite((((~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))))),
% 0.54/0.60 inference(bind,[status(th)],[])).
% 0.54/0.60 tff(107,plain,
% 0.54/0.60 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.54/0.60 inference(quant_intro,[status(thm)],[106])).
% 0.54/0.60 tff(108,axiom,(![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) | (~iLEQ(suc(B_11), suc(B_12))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_96')).
% 0.54/0.60 tff(109,plain,
% 0.54/0.60 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.54/0.60 tff(110,plain,
% 0.54/0.60 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.54/0.60 tff(111,plain,(
% 0.54/0.60 ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.54/0.60 inference(skolemize,[status(sab)],[110])).
% 0.54/0.60 tff(112,plain,
% 0.54/0.60 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.54/0.60 tff(113,plain,
% 0.54/0.60 (((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(114,plain,
% 0.54/0.60 (((~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)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(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(suc(z))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(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(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(115,plain,
% 0.54/0.60 (((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | ((~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)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(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(suc(z))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))) <=> ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~iLEQ(suc(z), suc(z)))))),
% 0.54/0.60 inference(monotonicity,[status(thm)],[114])).
% 0.54/0.60 tff(116,plain,
% 0.54/0.60 (((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | ((~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)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(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(suc(z))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))) <=> ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.54/0.60 inference(transitivity,[status(thm)],[115, 113])).
% 0.54/0.60 tff(117,plain,
% 0.54/0.60 ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | ((~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)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(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(suc(z))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))),
% 0.54/0.60 inference(quant_inst,[status(thm)],[])).
% 0.54/0.60 tff(118,plain,
% 0.54/0.60 ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 0.54/0.60 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.54/0.60 tff(119,plain,
% 0.54/0.60 (~tptp_fun__E_(f(z), f(suc(z)))),
% 0.54/0.60 inference(unit_resolution,[status(thm)],[118, 112, 49, 30, 83, 102])).
% 0.54/0.60 tff(120,plain,
% 0.54/0.60 (^[B_11: $i, B_13: $i, A_1: $i, B_12: $i] : refl((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))),
% 0.54/0.60 inference(bind,[status(th)],[])).
% 0.54/0.60 tff(121,plain,
% 0.54/0.60 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) <=> ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.54/0.60 inference(quant_intro,[status(thm)],[120])).
% 0.54/0.60 tff(122,plain,
% 0.54/0.60 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) <=> ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.54/0.60 inference(rewrite,[status(thm)],[])).
% 0.54/0.60 tff(123,plain,
% 0.54/0.60 (^[B_11: $i, B_13: $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(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) <=> ((~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> (((~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))))), rewrite((((~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(B_11)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) <=> ((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) <=> ((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> (((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(A_1)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) <=> (((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(B_13)))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(B_13)))) <=> ((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) <=> ((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) <=> (((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) <=> (((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))))), rewrite((((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(B_12)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) <=> ((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) <=> ((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> (((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~iLEQ(suc(B_11), suc(B_12)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))))), rewrite((((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'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))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'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))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'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))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | tptp_fun__E_(f(B_12), f(suc(B_12)))))), rewrite(((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | tptp_fun__E_(f(B_12), f(suc(B_12)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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_13), f(suc(B_13)))) <=> ((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | tptp_fun__E_(f(B_13), f(suc(B_13)))))), rewrite(((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | tptp_fun__E_(f(B_13), f(suc(B_13)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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_13), f(suc(B_13)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))))),
% 0.54/0.61 inference(bind,[status(th)],[])).
% 0.54/0.61 tff(124,plain,
% 0.54/0.61 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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_13), f(suc(B_13)))) <=> ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.54/0.61 inference(quant_intro,[status(thm)],[123])).
% 0.54/0.61 tff(125,axiom,(![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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_13), f(suc(B_13))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_16')).
% 0.54/0.61 tff(126,plain,
% 0.54/0.61 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.54/0.61 tff(127,plain,
% 0.54/0.61 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.54/0.61 tff(128,plain,(
% 0.54/0.61 ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.54/0.61 inference(skolemize,[status(sab)],[127])).
% 0.54/0.61 tff(129,plain,
% 0.54/0.61 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.54/0.61 tff(130,plain,
% 0.54/0.61 (((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | ((~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(131,plain,
% 0.54/0.61 ((tptp_fun__E_(f(z), f(suc(z))) | (~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)))) | (~iLEQ(suc(z), 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(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(132,plain,
% 0.54/0.61 (((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | (~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)))) | (~iLEQ(suc(z), 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(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | ((~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))))),
% 0.54/0.62 inference(monotonicity,[status(thm)],[131])).
% 0.54/0.62 tff(133,plain,
% 0.54/0.62 (((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | (~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)))) | (~iLEQ(suc(z), 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(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.54/0.62 inference(transitivity,[status(thm)],[132, 130])).
% 0.54/0.62 tff(134,plain,
% 0.54/0.62 ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | (~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)))) | (~iLEQ(suc(z), 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(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.54/0.62 inference(quant_inst,[status(thm)],[])).
% 0.54/0.62 tff(135,plain,
% 0.54/0.62 ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 0.54/0.62 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.54/0.62 tff(136,plain,
% 0.54/0.62 ($false),
% 0.54/0.62 inference(unit_resolution,[status(thm)],[135, 129, 49, 30, 102, 119])).
% 0.54/0.62 % SZS output end Proof
%------------------------------------------------------------------------------