TSTP Solution File: SYO683-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO683-1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 01:41:20 EDT 2022
% Result : Unsatisfiable 3.85s 2.68s
% Output : Proof 3.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYO683-1 : TPTP v8.1.0. Released v7.3.0.
% 0.08/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n008.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 15:52:10 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 3.85/2.68 % SZS status Unsatisfiable
% 3.85/2.68 % SZS output start Proof
% 3.85/2.68 tff(iLEQ_type, type, (
% 3.85/2.68 iLEQ: ( $i * $i ) > $o)).
% 3.85/2.68 tff(suc_type, type, (
% 3.85/2.68 suc: $i > $i)).
% 3.85/2.68 tff(z_type, type, (
% 3.85/2.68 z: $i)).
% 3.85/2.68 tff(tptp_fun__LE__type, type, (
% 3.85/2.68 tptp_fun__LE_: ( $i * $i ) > $o)).
% 3.85/2.68 tff(s_type, type, (
% 3.85/2.68 s: $i > $i)).
% 3.85/2.68 tff(tptp_fun__0__type, type, (
% 3.85/2.68 tptp_fun__0_: $i)).
% 3.85/2.68 tff(f_type, type, (
% 3.85/2.68 f: $i > $i)).
% 3.85/2.68 tff(tptp_fun__E__type, type, (
% 3.85/2.68 tptp_fun__E_: ( $i * $i ) > $o)).
% 3.85/2.68 tff(1,assumption,(~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))), introduced(assumption)).
% 3.85/2.68 tff(2,assumption,(~tptp_fun__LE_(f(z), s(|'0'|))), introduced(assumption)).
% 3.85/2.68 tff(3,plain,
% 3.85/2.68 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(s(s(s(|'0'|))))) <=> tptp_fun__LE_(f(A), s(s(s(s(|'0'|))))))),
% 3.85/2.68 inference(bind,[status(th)],[])).
% 3.85/2.68 tff(4,plain,
% 3.85/2.68 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|))))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 3.85/2.68 inference(quant_intro,[status(thm)],[3])).
% 3.85/2.68 tff(5,plain,
% 3.85/2.68 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|))))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 3.85/2.68 inference(rewrite,[status(thm)],[])).
% 3.85/2.68 tff(6,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_451')).
% 3.85/2.68 tff(7,plain,
% 3.85/2.68 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 3.85/2.68 inference(modus_ponens,[status(thm)],[6, 5])).
% 3.85/2.68 tff(8,plain,(
% 3.85/2.68 ![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 3.85/2.68 inference(skolemize,[status(sab)],[7])).
% 3.85/2.68 tff(9,plain,
% 3.85/2.68 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 3.85/2.68 inference(modus_ponens,[status(thm)],[8, 4])).
% 3.85/2.68 tff(10,plain,
% 3.85/2.68 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))),
% 3.85/2.68 inference(quant_inst,[status(thm)],[])).
% 3.85/2.68 tff(11,plain,
% 3.85/2.68 (tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))),
% 3.85/2.68 inference(unit_resolution,[status(thm)],[10, 9])).
% 3.85/2.68 tff(12,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))), introduced(assumption)).
% 3.85/2.68 tff(13,plain,
% 3.85/2.68 (^[B_158: $i] : refl((tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))) <=> (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))))),
% 3.85/2.68 inference(bind,[status(th)],[])).
% 3.85/2.68 tff(14,plain,
% 3.85/2.68 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 3.85/2.68 inference(quant_intro,[status(thm)],[13])).
% 3.85/2.68 tff(15,plain,
% 3.85/2.68 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 3.85/2.68 inference(rewrite,[status(thm)],[])).
% 3.85/2.68 tff(16,plain,
% 3.85/2.68 (^[B_158: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))) | tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))))),
% 3.85/2.68 inference(bind,[status(th)],[])).
% 3.85/2.68 tff(17,plain,
% 3.85/2.68 (![B_158: $i] : (((~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))) | tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 3.85/2.68 inference(quant_intro,[status(thm)],[16])).
% 3.85/2.68 tff(18,axiom,(![B_158: $i] : (((~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))) | tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_443')).
% 3.85/2.69 tff(19,plain,
% 3.85/2.69 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[18, 17])).
% 3.85/2.69 tff(20,plain,
% 3.85/2.69 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[19, 15])).
% 3.85/2.69 tff(21,plain,(
% 3.85/2.69 ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 3.85/2.69 inference(skolemize,[status(sab)],[20])).
% 3.85/2.69 tff(22,plain,
% 3.85/2.69 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[21, 14])).
% 3.85/2.69 tff(23,plain,
% 3.85/2.69 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))),
% 3.85/2.69 inference(rewrite,[status(thm)],[])).
% 3.85/2.69 tff(24,plain,
% 3.85/2.69 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))),
% 3.85/2.69 inference(quant_inst,[status(thm)],[])).
% 3.85/2.69 tff(25,plain,
% 3.85/2.69 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[24, 23])).
% 3.85/2.69 tff(26,plain,
% 3.85/2.69 (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 3.85/2.69 inference(unit_resolution,[status(thm)],[25, 22])).
% 3.85/2.69 tff(27,plain,
% 3.85/2.69 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 3.85/2.69 inference(unit_resolution,[status(thm)],[26, 12, 11])).
% 3.85/2.69 tff(28,plain,
% 3.85/2.69 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))),
% 3.85/2.69 inference(quant_inst,[status(thm)],[])).
% 3.85/2.69 tff(29,plain,
% 3.85/2.69 (tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))),
% 3.85/2.69 inference(unit_resolution,[status(thm)],[28, 9])).
% 3.85/2.69 tff(30,plain,
% 3.85/2.69 (^[B_158: $i] : refl((tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))) <=> (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))))),
% 3.85/2.69 inference(bind,[status(th)],[])).
% 3.85/2.69 tff(31,plain,
% 3.85/2.69 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 3.85/2.69 inference(quant_intro,[status(thm)],[30])).
% 3.85/2.69 tff(32,plain,
% 3.85/2.69 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 3.85/2.69 inference(rewrite,[status(thm)],[])).
% 3.85/2.69 tff(33,plain,
% 3.85/2.69 (^[B_158: $i] : rewrite((((~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))) | tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))))),
% 3.85/2.69 inference(bind,[status(th)],[])).
% 3.85/2.69 tff(34,plain,
% 3.85/2.69 (![B_158: $i] : (((~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))) | tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 3.85/2.69 inference(quant_intro,[status(thm)],[33])).
% 3.85/2.69 tff(35,axiom,(![B_158: $i] : (((~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))) | tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_539')).
% 3.85/2.69 tff(36,plain,
% 3.85/2.69 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[35, 34])).
% 3.85/2.69 tff(37,plain,
% 3.85/2.69 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[36, 32])).
% 3.85/2.69 tff(38,plain,(
% 3.85/2.69 ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 3.85/2.69 inference(skolemize,[status(sab)],[37])).
% 3.85/2.69 tff(39,plain,
% 3.85/2.69 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[38, 31])).
% 3.85/2.69 tff(40,plain,
% 3.85/2.69 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))),
% 3.85/2.69 inference(rewrite,[status(thm)],[])).
% 3.85/2.69 tff(41,plain,
% 3.85/2.69 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))),
% 3.85/2.69 inference(quant_inst,[status(thm)],[])).
% 3.85/2.69 tff(42,plain,
% 3.85/2.69 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[41, 40])).
% 3.85/2.69 tff(43,plain,
% 3.85/2.69 ((~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 3.85/2.69 inference(unit_resolution,[status(thm)],[42, 39, 12])).
% 3.85/2.69 tff(44,plain,
% 3.85/2.69 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 3.85/2.69 inference(unit_resolution,[status(thm)],[43, 29])).
% 3.85/2.69 tff(45,plain,
% 3.85/2.69 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))))),
% 3.85/2.69 inference(bind,[status(th)],[])).
% 3.85/2.69 tff(46,plain,
% 3.85/2.69 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 3.85/2.69 inference(quant_intro,[status(thm)],[45])).
% 3.85/2.69 tff(47,plain,
% 3.85/2.69 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 3.85/2.69 inference(rewrite,[status(thm)],[])).
% 3.85/2.69 tff(48,plain,
% 3.85/2.69 (^[A_1: $i] : rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))))),
% 3.85/2.69 inference(bind,[status(th)],[])).
% 3.85/2.69 tff(49,plain,
% 3.85/2.69 (![A_1: $i] : (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 3.85/2.69 inference(quant_intro,[status(thm)],[48])).
% 3.85/2.69 tff(50,axiom,(![A_1: $i] : (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_59')).
% 3.85/2.69 tff(51,plain,
% 3.85/2.69 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[50, 49])).
% 3.85/2.69 tff(52,plain,
% 3.85/2.69 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[51, 47])).
% 3.85/2.69 tff(53,plain,(
% 3.85/2.69 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 3.85/2.69 inference(skolemize,[status(sab)],[52])).
% 3.85/2.69 tff(54,plain,
% 3.85/2.69 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 3.85/2.69 inference(modus_ponens,[status(thm)],[53, 46])).
% 3.85/2.69 tff(55,plain,
% 3.85/2.69 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))),
% 3.85/2.69 inference(rewrite,[status(thm)],[])).
% 3.85/2.69 tff(56,plain,
% 3.85/2.69 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))),
% 3.85/2.69 inference(rewrite,[status(thm)],[])).
% 3.85/2.69 tff(57,plain,
% 3.85/2.69 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))))),
% 3.85/2.69 inference(monotonicity,[status(thm)],[56])).
% 3.85/2.69 tff(58,plain,
% 3.85/2.69 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))),
% 3.85/2.69 inference(transitivity,[status(thm)],[57, 55])).
% 3.85/2.69 tff(59,plain,
% 3.89/2.69 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))))),
% 3.89/2.69 inference(quant_inst,[status(thm)],[])).
% 3.89/2.69 tff(60,plain,
% 3.89/2.69 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))),
% 3.89/2.69 inference(modus_ponens,[status(thm)],[59, 58])).
% 3.89/2.69 tff(61,plain,
% 3.89/2.69 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))),
% 3.89/2.69 inference(unit_resolution,[status(thm)],[60, 54])).
% 3.89/2.69 tff(62,plain,
% 3.89/2.69 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 3.89/2.69 inference(unit_resolution,[status(thm)],[61, 44, 27])).
% 3.89/2.69 tff(63,plain,
% 3.89/2.69 (^[B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : refl(((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) <=> ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))),
% 3.89/2.69 inference(bind,[status(th)],[])).
% 3.89/2.69 tff(64,plain,
% 3.89/2.69 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) <=> ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 3.89/2.69 inference(quant_intro,[status(thm)],[63])).
% 3.89/2.69 tff(65,plain,
% 3.89/2.69 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) <=> ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 3.89/2.69 inference(rewrite,[status(thm)],[])).
% 3.89/2.69 tff(66,plain,
% 3.89/2.69 (^[B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(B_160), suc(B_161)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(B_160), suc(B_161)))) <=> ((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) <=> ((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), (((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) <=> (((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))))), rewrite((((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), (((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), ((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), (((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), (((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), ((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), (((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(B_159), suc(B_160)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(B_159), suc(B_160)))) <=> ((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), (((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) <=> ((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), ((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> (((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))))), rewrite((((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), (((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), (((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), ((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(B_161), suc(B_162)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(B_161), suc(B_162)))) <=> ((~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) <=> ((~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), (((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) <=> (((~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))))), rewrite((((~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), (((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), ((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), (((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(A_1), suc(B_159)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), (((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))))),
% 3.89/2.70 inference(bind,[status(th)],[])).
% 3.89/2.70 tff(67,plain,
% 3.89/2.70 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 3.89/2.70 inference(quant_intro,[status(thm)],[66])).
% 3.89/2.70 tff(68,axiom,(![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_159))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_560')).
% 3.89/2.70 tff(69,plain,
% 3.89/2.70 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 3.89/2.70 inference(modus_ponens,[status(thm)],[68, 67])).
% 3.89/2.70 tff(70,plain,
% 3.89/2.70 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 3.89/2.70 inference(modus_ponens,[status(thm)],[69, 65])).
% 3.89/2.70 tff(71,plain,(
% 3.89/2.70 ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 3.89/2.70 inference(skolemize,[status(sab)],[70])).
% 3.89/2.70 tff(72,plain,
% 3.89/2.70 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 3.89/2.70 inference(modus_ponens,[status(thm)],[71, 64])).
% 3.89/2.70 tff(73,plain,
% 3.89/2.70 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.89/2.70 inference(rewrite,[status(thm)],[])).
% 3.89/2.70 tff(74,plain,
% 3.89/2.70 (((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.89/2.70 inference(rewrite,[status(thm)],[])).
% 3.89/2.70 tff(75,plain,
% 3.89/2.70 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 3.89/2.70 inference(monotonicity,[status(thm)],[74])).
% 3.89/2.70 tff(76,plain,
% 3.89/2.70 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.89/2.70 inference(transitivity,[status(thm)],[75, 73])).
% 3.89/2.70 tff(77,plain,
% 3.89/2.70 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))),
% 3.89/2.70 inference(quant_inst,[status(thm)],[])).
% 3.89/2.70 tff(78,plain,
% 3.89/2.70 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 3.89/2.70 inference(modus_ponens,[status(thm)],[77, 76])).
% 3.89/2.70 tff(79,plain,
% 3.89/2.70 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 3.89/2.70 inference(unit_resolution,[status(thm)],[78, 72])).
% 3.89/2.70 tff(80,plain,
% 3.89/2.70 ($false),
% 3.89/2.70 inference(unit_resolution,[status(thm)],[79, 62, 44, 27])).
% 3.89/2.70 tff(81,plain,(tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 3.89/2.70 tff(82,plain,
% 3.89/2.70 (^[B_247: $i] : refl((tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|)))))) <=> (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|)))))))),
% 3.89/2.70 inference(bind,[status(th)],[])).
% 3.89/2.70 tff(83,plain,
% 3.89/2.70 (![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|)))))) <=> ![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 3.89/2.70 inference(quant_intro,[status(thm)],[82])).
% 3.89/2.70 tff(84,plain,
% 3.89/2.70 (![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|)))))) <=> ![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 3.89/2.70 inference(rewrite,[status(thm)],[])).
% 3.89/2.70 tff(85,plain,
% 3.89/2.70 (^[B_247: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247)))) | tptp_fun__LE_(f(B_247), s(s(|'0'|)))) <=> (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|)))))))),
% 3.89/2.70 inference(bind,[status(th)],[])).
% 3.89/2.70 tff(86,plain,
% 3.89/2.70 (![B_247: $i] : (((~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247)))) | tptp_fun__LE_(f(B_247), s(s(|'0'|)))) <=> ![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 3.89/2.70 inference(quant_intro,[status(thm)],[85])).
% 3.89/2.70 tff(87,axiom,(![B_247: $i] : (((~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247)))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_476')).
% 3.89/2.70 tff(88,plain,
% 3.89/2.70 (![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 3.89/2.70 inference(modus_ponens,[status(thm)],[87, 86])).
% 3.89/2.70 tff(89,plain,
% 3.89/2.70 (![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 3.89/2.70 inference(modus_ponens,[status(thm)],[88, 84])).
% 3.89/2.70 tff(90,plain,(
% 3.89/2.70 ![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 3.89/2.70 inference(skolemize,[status(sab)],[89])).
% 3.89/2.70 tff(91,plain,
% 3.89/2.70 (![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 3.89/2.70 inference(modus_ponens,[status(thm)],[90, 83])).
% 3.89/2.70 tff(92,plain,
% 3.89/2.70 (((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))) <=> ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 3.89/2.70 inference(rewrite,[status(thm)],[])).
% 3.89/2.70 tff(93,plain,
% 3.89/2.70 ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 3.89/2.70 inference(quant_inst,[status(thm)],[])).
% 3.89/2.70 tff(94,plain,
% 3.89/2.70 ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 3.89/2.70 inference(modus_ponens,[status(thm)],[93, 92])).
% 3.89/2.70 tff(95,plain,
% 3.89/2.70 (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 3.89/2.70 inference(unit_resolution,[status(thm)],[94, 91])).
% 3.89/2.70 tff(96,plain,
% 3.89/2.70 (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 3.89/2.70 inference(unit_resolution,[status(thm)],[95, 81])).
% 3.89/2.70 tff(97,plain,
% 3.89/2.70 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 3.89/2.70 inference(unit_resolution,[status(thm)],[96, 1])).
% 3.89/2.70 tff(98,plain,
% 3.89/2.70 (^[B_291: $i] : refl((tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|))))) <=> (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|))))))),
% 3.89/2.70 inference(bind,[status(th)],[])).
% 3.89/2.70 tff(99,plain,
% 3.89/2.70 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|))))) <=> ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 3.89/2.70 inference(quant_intro,[status(thm)],[98])).
% 3.89/2.70 tff(100,plain,
% 3.89/2.70 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|))))) <=> ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 3.89/2.70 inference(rewrite,[status(thm)],[])).
% 3.89/2.70 tff(101,plain,
% 3.89/2.70 (^[B_291: $i] : rewrite((((~tptp_fun__LE_(f(B_291), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|))) <=> (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|))))))),
% 3.89/2.70 inference(bind,[status(th)],[])).
% 3.89/2.70 tff(102,plain,
% 3.89/2.70 (![B_291: $i] : (((~tptp_fun__LE_(f(B_291), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|))) <=> ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 3.89/2.71 inference(quant_intro,[status(thm)],[101])).
% 3.89/2.71 tff(103,axiom,(![B_291: $i] : (((~tptp_fun__LE_(f(B_291), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_44')).
% 3.89/2.71 tff(104,plain,
% 3.89/2.71 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[103, 102])).
% 3.89/2.71 tff(105,plain,
% 3.89/2.71 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[104, 100])).
% 3.89/2.71 tff(106,plain,(
% 3.89/2.71 ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 3.89/2.71 inference(skolemize,[status(sab)],[105])).
% 3.89/2.71 tff(107,plain,
% 3.89/2.71 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[106, 99])).
% 3.89/2.71 tff(108,plain,
% 3.89/2.71 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))),
% 3.89/2.71 inference(rewrite,[status(thm)],[])).
% 3.89/2.71 tff(109,plain,
% 3.89/2.71 ((tptp_fun__E_(s(|'0'|), f(z)) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))),
% 3.89/2.71 inference(rewrite,[status(thm)],[])).
% 3.89/2.71 tff(110,plain,
% 3.89/2.71 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(z)) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))))),
% 3.89/2.71 inference(monotonicity,[status(thm)],[109])).
% 3.89/2.71 tff(111,plain,
% 3.89/2.71 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(z)) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))),
% 3.89/2.71 inference(transitivity,[status(thm)],[110, 108])).
% 3.89/2.71 tff(112,plain,
% 3.89/2.71 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(z)) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))),
% 3.89/2.71 inference(quant_inst,[status(thm)],[])).
% 3.89/2.71 tff(113,plain,
% 3.89/2.71 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[112, 111])).
% 3.89/2.71 tff(114,plain,
% 3.89/2.71 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))),
% 3.89/2.71 inference(unit_resolution,[status(thm)],[113, 107])).
% 3.89/2.71 tff(115,plain,
% 3.89/2.71 (tptp_fun__E_(s(|'0'|), f(z))),
% 3.89/2.71 inference(unit_resolution,[status(thm)],[114, 97, 2])).
% 3.89/2.71 tff(116,plain,
% 3.89/2.71 (^[B_247: $i] : refl(((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))) <=> ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))))),
% 3.89/2.71 inference(bind,[status(th)],[])).
% 3.89/2.71 tff(117,plain,
% 3.89/2.71 (![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))) <=> ![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 3.89/2.71 inference(quant_intro,[status(thm)],[116])).
% 3.89/2.71 tff(118,plain,
% 3.89/2.71 (![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))) <=> ![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 3.89/2.71 inference(rewrite,[status(thm)],[])).
% 3.89/2.71 tff(119,plain,
% 3.89/2.71 (^[B_247: $i] : rewrite((((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))) | tptp_fun__LE_(f(B_247), s(s(|'0'|)))) <=> ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))))),
% 3.89/2.71 inference(bind,[status(th)],[])).
% 3.89/2.71 tff(120,plain,
% 3.89/2.71 (![B_247: $i] : (((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))) | tptp_fun__LE_(f(B_247), s(s(|'0'|)))) <=> ![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 3.89/2.71 inference(quant_intro,[status(thm)],[119])).
% 3.89/2.71 tff(121,axiom,(![B_247: $i] : (((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_97')).
% 3.89/2.71 tff(122,plain,
% 3.89/2.71 (![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[121, 120])).
% 3.89/2.71 tff(123,plain,
% 3.89/2.71 (![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[122, 118])).
% 3.89/2.71 tff(124,plain,(
% 3.89/2.71 ![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 3.89/2.71 inference(skolemize,[status(sab)],[123])).
% 3.89/2.71 tff(125,plain,
% 3.89/2.71 (![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[124, 117])).
% 3.89/2.71 tff(126,plain,
% 3.89/2.71 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 3.89/2.71 inference(rewrite,[status(thm)],[])).
% 3.89/2.71 tff(127,plain,
% 3.89/2.71 (((~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) <=> (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 3.89/2.71 inference(rewrite,[status(thm)],[])).
% 3.89/2.71 tff(128,plain,
% 3.89/2.71 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))))),
% 3.89/2.71 inference(monotonicity,[status(thm)],[127])).
% 3.89/2.71 tff(129,plain,
% 3.89/2.71 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 3.89/2.71 inference(transitivity,[status(thm)],[128, 126])).
% 3.89/2.71 tff(130,plain,
% 3.89/2.71 ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))))),
% 3.89/2.71 inference(quant_inst,[status(thm)],[])).
% 3.89/2.71 tff(131,plain,
% 3.89/2.71 ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[130, 129])).
% 3.89/2.71 tff(132,plain,
% 3.89/2.71 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 3.89/2.71 inference(unit_resolution,[status(thm)],[131, 125, 81])).
% 3.89/2.71 tff(133,plain,
% 3.89/2.71 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 3.89/2.71 inference(unit_resolution,[status(thm)],[132, 1])).
% 3.89/2.71 tff(134,plain,
% 3.89/2.71 (^[B_291: $i] : refl((tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|))))) <=> (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|))))))),
% 3.89/2.71 inference(bind,[status(th)],[])).
% 3.89/2.71 tff(135,plain,
% 3.89/2.71 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|))))) <=> ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 3.89/2.71 inference(quant_intro,[status(thm)],[134])).
% 3.89/2.71 tff(136,plain,
% 3.89/2.71 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|))))) <=> ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 3.89/2.71 inference(rewrite,[status(thm)],[])).
% 3.89/2.71 tff(137,plain,
% 3.89/2.71 (^[B_291: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_291)))) | tptp_fun__LE_(f(B_291), s(|'0'|))) <=> (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|))))))),
% 3.89/2.71 inference(bind,[status(th)],[])).
% 3.89/2.71 tff(138,plain,
% 3.89/2.71 (![B_291: $i] : (((~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_291)))) | tptp_fun__LE_(f(B_291), s(|'0'|))) <=> ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 3.89/2.71 inference(quant_intro,[status(thm)],[137])).
% 3.89/2.71 tff(139,axiom,(![B_291: $i] : (((~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_291)))) | tptp_fun__LE_(f(B_291), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_222')).
% 3.89/2.71 tff(140,plain,
% 3.89/2.71 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[139, 138])).
% 3.89/2.71 tff(141,plain,
% 3.89/2.71 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[140, 136])).
% 3.89/2.71 tff(142,plain,(
% 3.89/2.71 ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 3.89/2.71 inference(skolemize,[status(sab)],[141])).
% 3.89/2.71 tff(143,plain,
% 3.89/2.71 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[142, 135])).
% 3.89/2.71 tff(144,plain,
% 3.89/2.71 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 3.89/2.71 inference(rewrite,[status(thm)],[])).
% 3.89/2.71 tff(145,plain,
% 3.89/2.71 ((tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 3.89/2.71 inference(rewrite,[status(thm)],[])).
% 3.89/2.71 tff(146,plain,
% 3.89/2.71 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))))),
% 3.89/2.71 inference(monotonicity,[status(thm)],[145])).
% 3.89/2.71 tff(147,plain,
% 3.89/2.71 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 3.89/2.71 inference(transitivity,[status(thm)],[146, 144])).
% 3.89/2.71 tff(148,plain,
% 3.89/2.71 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 3.89/2.71 inference(quant_inst,[status(thm)],[])).
% 3.89/2.71 tff(149,plain,
% 3.89/2.71 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[148, 147])).
% 3.89/2.71 tff(150,plain,
% 3.89/2.71 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 3.89/2.71 inference(unit_resolution,[status(thm)],[149, 143])).
% 3.89/2.71 tff(151,plain,
% 3.89/2.71 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 3.89/2.71 inference(unit_resolution,[status(thm)],[150, 133, 2])).
% 3.89/2.71 tff(152,plain,
% 3.89/2.71 (^[A_3: $i] : refl((iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))))),
% 3.89/2.71 inference(bind,[status(th)],[])).
% 3.89/2.71 tff(153,plain,
% 3.89/2.71 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 3.89/2.71 inference(quant_intro,[status(thm)],[152])).
% 3.89/2.71 tff(154,plain,
% 3.89/2.71 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 3.89/2.71 inference(rewrite,[status(thm)],[])).
% 3.89/2.71 tff(155,plain,
% 3.89/2.71 (^[A_3: $i] : rewrite((((~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | iLEQ(suc(A_3), suc(A_3))) <=> (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))))),
% 3.89/2.71 inference(bind,[status(th)],[])).
% 3.89/2.71 tff(156,plain,
% 3.89/2.71 (![A_3: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | iLEQ(suc(A_3), suc(A_3))) <=> ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 3.89/2.71 inference(quant_intro,[status(thm)],[155])).
% 3.89/2.71 tff(157,axiom,(![A_3: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | iLEQ(suc(A_3), suc(A_3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_398')).
% 3.89/2.71 tff(158,plain,
% 3.89/2.71 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[157, 156])).
% 3.89/2.71 tff(159,plain,
% 3.89/2.71 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[158, 154])).
% 3.89/2.71 tff(160,plain,(
% 3.89/2.71 ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 3.89/2.71 inference(skolemize,[status(sab)],[159])).
% 3.89/2.71 tff(161,plain,
% 3.89/2.71 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[160, 153])).
% 3.89/2.71 tff(162,plain,
% 3.89/2.71 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 3.89/2.71 inference(rewrite,[status(thm)],[])).
% 3.89/2.71 tff(163,plain,
% 3.89/2.71 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 3.89/2.71 inference(quant_inst,[status(thm)],[])).
% 3.89/2.71 tff(164,plain,
% 3.89/2.71 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 3.89/2.71 inference(modus_ponens,[status(thm)],[163, 162])).
% 3.89/2.71 tff(165,plain,
% 3.89/2.71 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 3.89/2.71 inference(unit_resolution,[status(thm)],[164, 161])).
% 3.89/2.71 tff(166,plain,
% 3.89/2.71 (iLEQ(suc(z), suc(z))),
% 3.89/2.71 inference(unit_resolution,[status(thm)],[165, 151, 115])).
% 3.89/2.71 tff(167,plain,
% 3.89/2.71 (^[B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : refl(((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))),
% 3.89/2.71 inference(bind,[status(th)],[])).
% 3.89/2.71 tff(168,plain,
% 3.89/2.71 (![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) <=> ![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 3.89/2.71 inference(quant_intro,[status(thm)],[167])).
% 3.89/2.71 tff(169,plain,
% 3.89/2.71 (![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) <=> ![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 3.89/2.71 inference(rewrite,[status(thm)],[])).
% 3.89/2.71 tff(170,plain,
% 3.89/2.71 (^[B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(A_3), suc(B_292)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(A_3), suc(B_292)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(B_294), suc(B_295)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(B_294), suc(B_295)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) | (~iLEQ(suc(B_293), suc(B_294)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(B_293), suc(B_294)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(B_293), suc(B_294)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) | (~iLEQ(suc(B_293), suc(B_294)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) | (~iLEQ(suc(B_293), suc(B_294)))) | (~iLEQ(suc(B_292), suc(B_293)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(B_292), suc(B_293)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(B_292), suc(B_293)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) | (~iLEQ(suc(B_293), suc(B_294)))) | (~iLEQ(suc(B_292), suc(B_293)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))))),
% 3.89/2.72 inference(bind,[status(th)],[])).
% 3.89/2.72 tff(171,plain,
% 3.89/2.72 (![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) | (~iLEQ(suc(B_293), suc(B_294)))) | (~iLEQ(suc(B_292), suc(B_293)))) <=> ![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 3.92/2.72 inference(quant_intro,[status(thm)],[170])).
% 3.92/2.72 tff(172,axiom,(![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) | (~iLEQ(suc(B_293), suc(B_294)))) | (~iLEQ(suc(B_292), suc(B_293))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_151')).
% 3.92/2.72 tff(173,plain,
% 3.92/2.72 (![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 3.92/2.72 inference(modus_ponens,[status(thm)],[172, 171])).
% 3.92/2.72 tff(174,plain,
% 3.92/2.72 (![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 3.92/2.72 inference(modus_ponens,[status(thm)],[173, 169])).
% 3.92/2.72 tff(175,plain,(
% 3.92/2.72 ![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 3.92/2.72 inference(skolemize,[status(sab)],[174])).
% 3.92/2.72 tff(176,plain,
% 3.92/2.72 (![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 3.92/2.72 inference(modus_ponens,[status(thm)],[175, 168])).
% 3.92/2.72 tff(177,plain,
% 3.92/2.72 (((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.92/2.72 inference(rewrite,[status(thm)],[])).
% 3.92/2.72 tff(178,plain,
% 3.92/2.72 (((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.92/2.72 inference(rewrite,[status(thm)],[])).
% 3.92/2.72 tff(179,plain,
% 3.92/2.72 (((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 3.92/2.72 inference(monotonicity,[status(thm)],[178])).
% 3.92/2.72 tff(180,plain,
% 3.92/2.72 (((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.92/2.72 inference(transitivity,[status(thm)],[179, 177])).
% 3.92/2.72 tff(181,plain,
% 3.92/2.72 ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 3.92/2.72 inference(quant_inst,[status(thm)],[])).
% 3.92/2.72 tff(182,plain,
% 3.92/2.72 ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 3.92/2.72 inference(modus_ponens,[status(thm)],[181, 180])).
% 3.92/2.72 tff(183,plain,
% 3.92/2.72 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 3.92/2.72 inference(unit_resolution,[status(thm)],[182, 176])).
% 3.92/2.72 tff(184,plain,
% 3.92/2.72 ($false),
% 3.92/2.72 inference(unit_resolution,[status(thm)],[183, 166, 151, 115])).
% 3.92/2.72 tff(185,plain,(tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | tptp_fun__LE_(f(z), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.72 tff(186,plain,
% 3.92/2.72 (tptp_fun__LE_(f(z), s(|'0'|))),
% 3.92/2.72 inference(unit_resolution,[status(thm)],[185, 1])).
% 3.92/2.72 tff(187,plain,
% 3.92/2.72 (^[B_309: $i] : refl((tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|)))) <=> (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|)))))),
% 3.92/2.72 inference(bind,[status(th)],[])).
% 3.92/2.72 tff(188,plain,
% 3.92/2.72 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|)))) <=> ![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 3.92/2.72 inference(quant_intro,[status(thm)],[187])).
% 3.92/2.72 tff(189,plain,
% 3.92/2.72 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|)))) <=> ![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 3.92/2.72 inference(rewrite,[status(thm)],[])).
% 3.92/2.72 tff(190,plain,
% 3.92/2.72 (^[B_309: $i] : rewrite((((~tptp_fun__LE_(f(B_309), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_309))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|)))))),
% 3.92/2.72 inference(bind,[status(th)],[])).
% 3.92/2.72 tff(191,plain,
% 3.92/2.72 (![B_309: $i] : (((~tptp_fun__LE_(f(B_309), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_309))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> ![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 3.92/2.72 inference(quant_intro,[status(thm)],[190])).
% 3.92/2.72 tff(192,axiom,(![B_309: $i] : (((~tptp_fun__LE_(f(B_309), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_309))) | tptp_fun__LE_(f(B_309), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_89')).
% 3.92/2.72 tff(193,plain,
% 3.92/2.72 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 3.92/2.72 inference(modus_ponens,[status(thm)],[192, 191])).
% 3.92/2.72 tff(194,plain,
% 3.92/2.72 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 3.92/2.72 inference(modus_ponens,[status(thm)],[193, 189])).
% 3.92/2.72 tff(195,plain,(
% 3.92/2.72 ![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 3.92/2.72 inference(skolemize,[status(sab)],[194])).
% 3.92/2.72 tff(196,plain,
% 3.92/2.72 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 3.92/2.72 inference(modus_ponens,[status(thm)],[195, 188])).
% 3.92/2.72 tff(197,plain,
% 3.92/2.72 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 3.92/2.72 inference(rewrite,[status(thm)],[])).
% 3.92/2.72 tff(198,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_287')).
% 3.92/2.72 tff(199,plain,
% 3.92/2.72 (~tptp_fun__LE_(f(z), |'0'|)),
% 3.92/2.72 inference(modus_ponens,[status(thm)],[198, 197])).
% 3.92/2.72 tff(200,plain,
% 3.92/2.72 (((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 3.92/2.72 inference(rewrite,[status(thm)],[])).
% 3.92/2.72 tff(201,plain,
% 3.92/2.72 ((tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|)))) <=> (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 3.92/2.72 inference(rewrite,[status(thm)],[])).
% 3.92/2.72 tff(202,plain,
% 3.92/2.72 (((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))))),
% 3.92/2.72 inference(monotonicity,[status(thm)],[201])).
% 3.92/2.72 tff(203,plain,
% 3.92/2.72 (((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 3.92/2.73 inference(transitivity,[status(thm)],[202, 200])).
% 3.92/2.73 tff(204,plain,
% 3.92/2.73 ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 3.92/2.73 inference(quant_inst,[status(thm)],[])).
% 3.92/2.73 tff(205,plain,
% 3.92/2.73 ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))),
% 3.92/2.73 inference(modus_ponens,[status(thm)],[204, 203])).
% 3.92/2.73 tff(206,plain,
% 3.92/2.73 (tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[205, 199, 196])).
% 3.92/2.73 tff(207,plain,
% 3.92/2.73 (tptp_fun__E_(|'0'|, f(z))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[206, 186])).
% 3.92/2.73 tff(208,assumption,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 3.92/2.73 tff(209,assumption,(~tptp_fun__LE_(f(suc(z)), s(|'0'|))), introduced(assumption)).
% 3.92/2.73 tff(210,plain,
% 3.92/2.73 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 3.92/2.73 inference(rewrite,[status(thm)],[])).
% 3.92/2.73 tff(211,plain,
% 3.92/2.73 ((tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 3.92/2.73 inference(rewrite,[status(thm)],[])).
% 3.92/2.73 tff(212,plain,
% 3.92/2.73 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))))),
% 3.92/2.73 inference(monotonicity,[status(thm)],[211])).
% 3.92/2.73 tff(213,plain,
% 3.92/2.73 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 3.92/2.73 inference(transitivity,[status(thm)],[212, 210])).
% 3.92/2.73 tff(214,plain,
% 3.92/2.73 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 3.92/2.73 inference(quant_inst,[status(thm)],[])).
% 3.92/2.73 tff(215,plain,
% 3.92/2.73 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 3.92/2.73 inference(modus_ponens,[status(thm)],[214, 213])).
% 3.92/2.73 tff(216,plain,
% 3.92/2.73 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[215, 107])).
% 3.92/2.73 tff(217,plain,
% 3.92/2.73 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[216, 209, 208])).
% 3.92/2.73 tff(218,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), introduced(assumption)).
% 3.92/2.73 tff(219,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), introduced(assumption)).
% 3.92/2.73 tff(220,plain,
% 3.92/2.73 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))),
% 3.92/2.73 inference(quant_inst,[status(thm)],[])).
% 3.92/2.73 tff(221,plain,
% 3.92/2.73 (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[220, 9])).
% 3.92/2.73 tff(222,plain,
% 3.92/2.73 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 3.92/2.73 inference(rewrite,[status(thm)],[])).
% 3.92/2.73 tff(223,plain,
% 3.92/2.73 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 3.92/2.73 inference(quant_inst,[status(thm)],[])).
% 3.92/2.73 tff(224,plain,
% 3.92/2.73 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 3.92/2.73 inference(modus_ponens,[status(thm)],[223, 222])).
% 3.92/2.73 tff(225,plain,
% 3.92/2.73 (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[224, 22])).
% 3.92/2.73 tff(226,plain,
% 3.92/2.73 (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[225, 221])).
% 3.92/2.73 tff(227,plain,
% 3.92/2.73 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[226, 219])).
% 3.92/2.73 tff(228,plain,
% 3.92/2.73 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))),
% 3.92/2.73 inference(rewrite,[status(thm)],[])).
% 3.92/2.73 tff(229,plain,
% 3.92/2.73 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))),
% 3.92/2.73 inference(quant_inst,[status(thm)],[])).
% 3.92/2.73 tff(230,plain,
% 3.92/2.73 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 3.92/2.73 inference(modus_ponens,[status(thm)],[229, 228])).
% 3.92/2.73 tff(231,plain,
% 3.92/2.73 ((~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[230, 39, 219])).
% 3.92/2.73 tff(232,plain,
% 3.92/2.73 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[231, 11])).
% 3.92/2.73 tff(233,plain,
% 3.92/2.73 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 3.92/2.73 inference(rewrite,[status(thm)],[])).
% 3.92/2.73 tff(234,plain,
% 3.92/2.73 (((~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 3.92/2.73 inference(rewrite,[status(thm)],[])).
% 3.92/2.73 tff(235,plain,
% 3.92/2.73 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))))),
% 3.92/2.73 inference(monotonicity,[status(thm)],[234])).
% 3.92/2.73 tff(236,plain,
% 3.92/2.73 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 3.92/2.73 inference(transitivity,[status(thm)],[235, 233])).
% 3.92/2.73 tff(237,plain,
% 3.92/2.73 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 3.92/2.73 inference(quant_inst,[status(thm)],[])).
% 3.92/2.73 tff(238,plain,
% 3.92/2.73 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 3.92/2.73 inference(modus_ponens,[status(thm)],[237, 236])).
% 3.92/2.73 tff(239,plain,
% 3.92/2.73 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[238, 72])).
% 3.92/2.73 tff(240,plain,
% 3.92/2.73 (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[239, 232, 227])).
% 3.92/2.73 tff(241,plain,
% 3.92/2.73 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 3.92/2.73 inference(rewrite,[status(thm)],[])).
% 3.92/2.73 tff(242,plain,
% 3.92/2.73 ((iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 3.92/2.73 inference(rewrite,[status(thm)],[])).
% 3.92/2.73 tff(243,plain,
% 3.92/2.73 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))))),
% 3.92/2.73 inference(monotonicity,[status(thm)],[242])).
% 3.92/2.73 tff(244,plain,
% 3.92/2.73 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 3.92/2.73 inference(transitivity,[status(thm)],[243, 241])).
% 3.92/2.73 tff(245,plain,
% 3.92/2.73 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))),
% 3.92/2.73 inference(quant_inst,[status(thm)],[])).
% 3.92/2.73 tff(246,plain,
% 3.92/2.73 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 3.92/2.73 inference(modus_ponens,[status(thm)],[245, 244])).
% 3.92/2.73 tff(247,plain,
% 3.92/2.73 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[246, 54])).
% 3.92/2.73 tff(248,plain,
% 3.92/2.73 ($false),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[247, 240, 232, 227])).
% 3.92/2.73 tff(249,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.73 tff(250,plain,
% 3.92/2.73 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 3.92/2.73 inference(rewrite,[status(thm)],[])).
% 3.92/2.73 tff(251,plain,
% 3.92/2.73 (((~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) <=> (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 3.92/2.73 inference(rewrite,[status(thm)],[])).
% 3.92/2.73 tff(252,plain,
% 3.92/2.73 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))))),
% 3.92/2.73 inference(monotonicity,[status(thm)],[251])).
% 3.92/2.73 tff(253,plain,
% 3.92/2.73 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 3.92/2.73 inference(transitivity,[status(thm)],[252, 250])).
% 3.92/2.73 tff(254,plain,
% 3.92/2.73 ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))),
% 3.92/2.73 inference(quant_inst,[status(thm)],[])).
% 3.92/2.73 tff(255,plain,
% 3.92/2.73 ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 3.92/2.73 inference(modus_ponens,[status(thm)],[254, 253])).
% 3.92/2.73 tff(256,plain,
% 3.92/2.73 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[255, 125, 249])).
% 3.92/2.73 tff(257,plain,
% 3.92/2.73 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[256, 218])).
% 3.92/2.73 tff(258,assumption,(~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))), introduced(assumption)).
% 3.92/2.73 tff(259,assumption,(~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 3.92/2.73 tff(260,plain,
% 3.92/2.73 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))),
% 3.92/2.73 inference(quant_inst,[status(thm)],[])).
% 3.92/2.73 tff(261,plain,
% 3.92/2.73 ($false),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[260, 9, 259])).
% 3.92/2.73 tff(262,plain,(tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.73 tff(263,plain,
% 3.92/2.73 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))),
% 3.92/2.73 inference(rewrite,[status(thm)],[])).
% 3.92/2.73 tff(264,plain,
% 3.92/2.73 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))),
% 3.92/2.73 inference(quant_inst,[status(thm)],[])).
% 3.92/2.73 tff(265,plain,
% 3.92/2.73 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))),
% 3.92/2.73 inference(modus_ponens,[status(thm)],[264, 263])).
% 3.92/2.73 tff(266,plain,
% 3.92/2.73 (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[265, 22, 262])).
% 3.92/2.73 tff(267,plain,
% 3.92/2.73 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))),
% 3.92/2.73 inference(unit_resolution,[status(thm)],[266, 258])).
% 3.92/2.73 tff(268,plain,
% 3.92/2.73 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 3.92/2.73 inference(rewrite,[status(thm)],[])).
% 3.92/2.73 tff(269,plain,
% 3.92/2.73 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 3.92/2.74 inference(quant_inst,[status(thm)],[])).
% 3.92/2.74 tff(270,plain,
% 3.92/2.74 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 3.92/2.74 inference(modus_ponens,[status(thm)],[269, 268])).
% 3.92/2.74 tff(271,plain,
% 3.92/2.74 (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 3.92/2.74 inference(unit_resolution,[status(thm)],[270, 39])).
% 3.92/2.74 tff(272,plain,
% 3.92/2.74 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 3.92/2.74 inference(unit_resolution,[status(thm)],[271, 258, 221])).
% 3.92/2.74 tff(273,plain,
% 3.92/2.74 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))))),
% 3.92/2.74 inference(rewrite,[status(thm)],[])).
% 3.92/2.74 tff(274,plain,
% 3.92/2.74 ((iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))))),
% 3.92/2.74 inference(rewrite,[status(thm)],[])).
% 3.92/2.74 tff(275,plain,
% 3.92/2.74 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))))),
% 3.92/2.74 inference(monotonicity,[status(thm)],[274])).
% 3.92/2.74 tff(276,plain,
% 3.92/2.74 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))))),
% 3.92/2.74 inference(transitivity,[status(thm)],[275, 273])).
% 3.92/2.74 tff(277,plain,
% 3.92/2.74 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 3.92/2.74 inference(quant_inst,[status(thm)],[])).
% 3.92/2.74 tff(278,plain,
% 3.92/2.74 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))),
% 3.92/2.74 inference(modus_ponens,[status(thm)],[277, 276])).
% 3.92/2.74 tff(279,plain,
% 3.92/2.74 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))),
% 3.92/2.74 inference(unit_resolution,[status(thm)],[278, 54])).
% 3.92/2.74 tff(280,plain,
% 3.92/2.74 (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))),
% 3.92/2.74 inference(unit_resolution,[status(thm)],[279, 272, 267])).
% 3.92/2.74 tff(281,plain,
% 3.92/2.74 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))),
% 3.92/2.74 inference(rewrite,[status(thm)],[])).
% 3.92/2.74 tff(282,plain,
% 3.92/2.74 (((~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))),
% 3.92/2.74 inference(rewrite,[status(thm)],[])).
% 3.92/2.74 tff(283,plain,
% 3.92/2.74 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))))))),
% 3.92/2.74 inference(monotonicity,[status(thm)],[282])).
% 3.92/2.74 tff(284,plain,
% 3.92/2.74 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))),
% 3.92/2.74 inference(transitivity,[status(thm)],[283, 281])).
% 3.92/2.74 tff(285,plain,
% 3.92/2.74 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))))),
% 3.92/2.74 inference(quant_inst,[status(thm)],[])).
% 3.92/2.74 tff(286,plain,
% 3.92/2.74 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))))),
% 3.92/2.74 inference(modus_ponens,[status(thm)],[285, 284])).
% 3.92/2.74 tff(287,plain,
% 3.92/2.74 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))))),
% 3.92/2.74 inference(unit_resolution,[status(thm)],[286, 72])).
% 3.92/2.74 tff(288,plain,
% 3.92/2.74 ($false),
% 3.92/2.74 inference(unit_resolution,[status(thm)],[287, 280, 272, 267])).
% 3.92/2.74 tff(289,plain,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.74 tff(290,plain,
% 3.92/2.74 (((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))))) <=> ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))))),
% 3.92/2.74 inference(rewrite,[status(thm)],[])).
% 3.92/2.74 tff(291,plain,
% 3.92/2.74 ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))))),
% 3.92/2.74 inference(quant_inst,[status(thm)],[])).
% 3.92/2.74 tff(292,plain,
% 3.92/2.74 ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 3.92/2.74 inference(modus_ponens,[status(thm)],[291, 290])).
% 3.92/2.74 tff(293,plain,
% 3.92/2.74 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 3.92/2.74 inference(unit_resolution,[status(thm)],[292, 91])).
% 3.92/2.74 tff(294,plain,
% 3.92/2.74 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))),
% 3.92/2.74 inference(unit_resolution,[status(thm)],[293, 289])).
% 3.92/2.74 tff(295,plain,
% 3.92/2.74 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))),
% 3.92/2.74 inference(unit_resolution,[status(thm)],[294, 218])).
% 3.92/2.74 tff(296,plain,
% 3.92/2.74 (^[A_2: $i] : refl((iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))))),
% 3.92/2.74 inference(bind,[status(th)],[])).
% 3.92/2.74 tff(297,plain,
% 3.92/2.74 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 3.92/2.74 inference(quant_intro,[status(thm)],[296])).
% 3.92/2.74 tff(298,plain,
% 3.92/2.74 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 3.92/2.74 inference(rewrite,[status(thm)],[])).
% 3.92/2.74 tff(299,plain,
% 3.92/2.74 (^[A_2: $i] : rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))))),
% 3.92/2.74 inference(bind,[status(th)],[])).
% 3.92/2.74 tff(300,plain,
% 3.92/2.74 (![A_2: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 3.92/2.74 inference(quant_intro,[status(thm)],[299])).
% 3.92/2.74 tff(301,axiom,(![A_2: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_29')).
% 3.92/2.74 tff(302,plain,
% 3.92/2.74 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 3.92/2.74 inference(modus_ponens,[status(thm)],[301, 300])).
% 3.92/2.74 tff(303,plain,
% 3.92/2.74 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 3.92/2.74 inference(modus_ponens,[status(thm)],[302, 298])).
% 3.92/2.74 tff(304,plain,(
% 3.92/2.74 ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 3.92/2.74 inference(skolemize,[status(sab)],[303])).
% 3.92/2.74 tff(305,plain,
% 3.92/2.74 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 3.92/2.74 inference(modus_ponens,[status(thm)],[304, 297])).
% 3.92/2.74 tff(306,plain,
% 3.92/2.74 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))))),
% 3.92/2.74 inference(rewrite,[status(thm)],[])).
% 3.92/2.74 tff(307,plain,
% 3.92/2.74 ((iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))))),
% 3.92/2.74 inference(rewrite,[status(thm)],[])).
% 3.92/2.74 tff(308,plain,
% 3.92/2.74 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))))))),
% 3.92/2.74 inference(monotonicity,[status(thm)],[307])).
% 3.92/2.74 tff(309,plain,
% 3.92/2.74 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))))),
% 3.92/2.74 inference(transitivity,[status(thm)],[308, 306])).
% 3.92/2.74 tff(310,plain,
% 3.92/2.74 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))),
% 3.92/2.74 inference(quant_inst,[status(thm)],[])).
% 3.92/2.74 tff(311,plain,
% 3.92/2.74 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))))),
% 3.92/2.74 inference(modus_ponens,[status(thm)],[310, 309])).
% 3.92/2.74 tff(312,plain,
% 3.92/2.74 ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))))),
% 3.92/2.74 inference(unit_resolution,[status(thm)],[311, 305])).
% 3.92/2.74 tff(313,plain,
% 3.92/2.74 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 3.92/2.74 inference(unit_resolution,[status(thm)],[312, 295, 257])).
% 3.92/2.74 tff(314,plain,
% 3.92/2.74 (^[B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : refl(((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))),
% 3.92/2.74 inference(bind,[status(th)],[])).
% 3.92/2.74 tff(315,plain,
% 3.92/2.74 (![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) <=> ![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 3.92/2.74 inference(quant_intro,[status(thm)],[314])).
% 3.92/2.74 tff(316,plain,
% 3.92/2.74 (![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) <=> ![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 3.92/2.74 inference(rewrite,[status(thm)],[])).
% 3.92/2.74 tff(317,plain,
% 3.92/2.74 (^[B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(A_2), suc(B_248)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(A_2), suc(B_248)))) <=> ((~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) <=> ((~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), (((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) <=> (((~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))))), rewrite((((~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), (((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), ((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), (((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(B_249), suc(B_250)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(B_249), suc(B_250)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), (((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), ((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), (((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), (((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), ((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), (((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), (((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), ((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(B_248), suc(B_249)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(B_248), suc(B_249)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), (((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), (((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), (((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) | (~iLEQ(suc(B_250), suc(B_251)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(B_250), suc(B_251)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(B_250), suc(B_251)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), (((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) | (~iLEQ(suc(B_250), suc(B_251)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))))),
% 3.92/2.75 inference(bind,[status(th)],[])).
% 3.92/2.75 tff(318,plain,
% 3.92/2.75 (![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) | (~iLEQ(suc(B_250), suc(B_251)))) <=> ![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 3.92/2.75 inference(quant_intro,[status(thm)],[317])).
% 3.92/2.75 tff(319,axiom,(![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) | (~iLEQ(suc(B_250), suc(B_251))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_563')).
% 3.92/2.75 tff(320,plain,
% 3.92/2.75 (![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 3.92/2.75 inference(modus_ponens,[status(thm)],[319, 318])).
% 3.92/2.75 tff(321,plain,
% 3.92/2.75 (![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 3.92/2.75 inference(modus_ponens,[status(thm)],[320, 316])).
% 3.92/2.75 tff(322,plain,(
% 3.92/2.75 ![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 3.92/2.75 inference(skolemize,[status(sab)],[321])).
% 3.92/2.75 tff(323,plain,
% 3.92/2.75 (![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 3.92/2.75 inference(modus_ponens,[status(thm)],[322, 315])).
% 3.92/2.75 tff(324,plain,
% 3.92/2.75 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 3.92/2.75 inference(rewrite,[status(thm)],[])).
% 3.92/2.75 tff(325,plain,
% 3.92/2.75 (((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 3.92/2.75 inference(rewrite,[status(thm)],[])).
% 3.92/2.75 tff(326,plain,
% 3.92/2.75 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))))),
% 3.92/2.75 inference(monotonicity,[status(thm)],[325])).
% 3.92/2.75 tff(327,plain,
% 3.92/2.75 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 3.92/2.75 inference(transitivity,[status(thm)],[326, 324])).
% 3.92/2.75 tff(328,plain,
% 3.92/2.75 ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))))),
% 3.92/2.76 inference(quant_inst,[status(thm)],[])).
% 3.92/2.76 tff(329,plain,
% 3.92/2.76 ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 3.92/2.76 inference(modus_ponens,[status(thm)],[328, 327])).
% 3.92/2.76 tff(330,plain,
% 3.92/2.76 ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[329, 323])).
% 3.92/2.76 tff(331,plain,
% 3.92/2.76 ($false),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[330, 313, 295, 257])).
% 3.92/2.76 tff(332,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.76 tff(333,plain,
% 3.92/2.76 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 3.92/2.76 inference(rewrite,[status(thm)],[])).
% 3.92/2.76 tff(334,plain,
% 3.92/2.76 ((tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 3.92/2.76 inference(rewrite,[status(thm)],[])).
% 3.92/2.76 tff(335,plain,
% 3.92/2.76 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))))),
% 3.92/2.76 inference(monotonicity,[status(thm)],[334])).
% 3.92/2.76 tff(336,plain,
% 3.92/2.76 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 3.92/2.76 inference(transitivity,[status(thm)],[335, 333])).
% 3.92/2.76 tff(337,plain,
% 3.92/2.76 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 3.92/2.76 inference(quant_inst,[status(thm)],[])).
% 3.92/2.76 tff(338,plain,
% 3.92/2.76 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 3.92/2.76 inference(modus_ponens,[status(thm)],[337, 336])).
% 3.92/2.76 tff(339,plain,
% 3.92/2.76 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[338, 143])).
% 3.92/2.76 tff(340,plain,
% 3.92/2.76 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[339, 332])).
% 3.92/2.76 tff(341,plain,
% 3.92/2.76 (tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[340, 209])).
% 3.92/2.76 tff(342,plain,
% 3.92/2.76 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 3.92/2.76 inference(rewrite,[status(thm)],[])).
% 3.92/2.76 tff(343,plain,
% 3.92/2.76 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 3.92/2.76 inference(rewrite,[status(thm)],[])).
% 3.92/2.76 tff(344,plain,
% 3.92/2.76 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))))),
% 3.92/2.76 inference(monotonicity,[status(thm)],[343])).
% 3.92/2.76 tff(345,plain,
% 3.92/2.76 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 3.92/2.76 inference(transitivity,[status(thm)],[344, 342])).
% 3.92/2.76 tff(346,plain,
% 3.92/2.76 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 3.92/2.76 inference(quant_inst,[status(thm)],[])).
% 3.92/2.76 tff(347,plain,
% 3.92/2.76 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 3.92/2.76 inference(modus_ponens,[status(thm)],[346, 345])).
% 3.92/2.76 tff(348,plain,
% 3.92/2.76 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[347, 161])).
% 3.92/2.76 tff(349,plain,
% 3.92/2.76 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[348, 341, 217])).
% 3.92/2.76 tff(350,plain,
% 3.92/2.76 (((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.92/2.76 inference(rewrite,[status(thm)],[])).
% 3.92/2.76 tff(351,plain,
% 3.92/2.76 (((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.92/2.76 inference(rewrite,[status(thm)],[])).
% 3.92/2.76 tff(352,plain,
% 3.92/2.76 (((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 3.92/2.76 inference(monotonicity,[status(thm)],[351])).
% 3.92/2.76 tff(353,plain,
% 3.92/2.76 (((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.92/2.76 inference(transitivity,[status(thm)],[352, 350])).
% 3.92/2.76 tff(354,plain,
% 3.92/2.76 ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 3.92/2.76 inference(quant_inst,[status(thm)],[])).
% 3.92/2.76 tff(355,plain,
% 3.92/2.76 ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 3.92/2.76 inference(modus_ponens,[status(thm)],[354, 353])).
% 3.92/2.76 tff(356,plain,
% 3.92/2.76 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[355, 176])).
% 3.92/2.76 tff(357,plain,
% 3.92/2.76 ($false),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[356, 349, 341, 217])).
% 3.92/2.76 tff(358,plain,(tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.76 tff(359,plain,
% 3.92/2.76 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[358, 133])).
% 3.92/2.76 tff(360,plain,
% 3.92/2.76 (^[B_309: $i] : refl((tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|)))),
% 3.92/2.76 inference(bind,[status(th)],[])).
% 3.92/2.76 tff(361,plain,
% 3.92/2.76 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> ![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 3.92/2.76 inference(quant_intro,[status(thm)],[360])).
% 3.92/2.76 tff(362,plain,
% 3.92/2.76 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> ![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 3.92/2.76 inference(rewrite,[status(thm)],[])).
% 3.92/2.76 tff(363,plain,
% 3.92/2.76 (^[B_309: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_309)))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|)))),
% 3.92/2.76 inference(bind,[status(th)],[])).
% 3.92/2.76 tff(364,plain,
% 3.92/2.76 (![B_309: $i] : (((~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_309)))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> ![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 3.92/2.76 inference(quant_intro,[status(thm)],[363])).
% 3.92/2.76 tff(365,axiom,(![B_309: $i] : (((~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_309)))) | tptp_fun__LE_(f(B_309), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_547')).
% 3.92/2.76 tff(366,plain,
% 3.92/2.76 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 3.92/2.76 inference(modus_ponens,[status(thm)],[365, 364])).
% 3.92/2.76 tff(367,plain,
% 3.92/2.76 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 3.92/2.76 inference(modus_ponens,[status(thm)],[366, 362])).
% 3.92/2.76 tff(368,plain,(
% 3.92/2.76 ![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 3.92/2.76 inference(skolemize,[status(sab)],[367])).
% 3.92/2.76 tff(369,plain,
% 3.92/2.76 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 3.92/2.76 inference(modus_ponens,[status(thm)],[368, 361])).
% 3.92/2.76 tff(370,plain,
% 3.92/2.76 (((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))) <=> ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 3.92/2.76 inference(rewrite,[status(thm)],[])).
% 3.92/2.76 tff(371,plain,
% 3.92/2.76 ((tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|)) <=> (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 3.92/2.76 inference(rewrite,[status(thm)],[])).
% 3.92/2.76 tff(372,plain,
% 3.92/2.76 (((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|))) <=> ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))))),
% 3.92/2.76 inference(monotonicity,[status(thm)],[371])).
% 3.92/2.76 tff(373,plain,
% 3.92/2.76 (((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|))) <=> ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 3.92/2.76 inference(transitivity,[status(thm)],[372, 370])).
% 3.92/2.76 tff(374,plain,
% 3.92/2.76 ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|))),
% 3.92/2.76 inference(quant_inst,[status(thm)],[])).
% 3.92/2.76 tff(375,plain,
% 3.92/2.76 ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 3.92/2.76 inference(modus_ponens,[status(thm)],[374, 373])).
% 3.92/2.76 tff(376,plain,
% 3.92/2.76 (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[375, 199, 369])).
% 3.92/2.76 tff(377,plain,
% 3.92/2.76 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[376, 359])).
% 3.92/2.76 tff(378,assumption,(tptp_fun__E_(|'0'|, f(z))), introduced(assumption)).
% 3.92/2.76 tff(379,assumption,(tptp_fun__E_(|'0'|, f(suc(z)))), introduced(assumption)).
% 3.92/2.76 tff(380,plain,
% 3.92/2.76 (^[A_4: $i] : refl((iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4)))))),
% 3.92/2.76 inference(bind,[status(th)],[])).
% 3.92/2.76 tff(381,plain,
% 3.92/2.76 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 3.92/2.76 inference(quant_intro,[status(thm)],[380])).
% 3.92/2.76 tff(382,plain,
% 3.92/2.76 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 3.92/2.76 inference(rewrite,[status(thm)],[])).
% 3.92/2.76 tff(383,plain,
% 3.92/2.76 (^[A_4: $i] : rewrite((((~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | iLEQ(suc(A_4), suc(A_4))) <=> (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4)))))),
% 3.92/2.76 inference(bind,[status(th)],[])).
% 3.92/2.76 tff(384,plain,
% 3.92/2.76 (![A_4: $i] : (((~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | iLEQ(suc(A_4), suc(A_4))) <=> ![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 3.92/2.76 inference(quant_intro,[status(thm)],[383])).
% 3.92/2.76 tff(385,axiom,(![A_4: $i] : (((~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | iLEQ(suc(A_4), suc(A_4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_469')).
% 3.92/2.76 tff(386,plain,
% 3.92/2.76 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 3.92/2.76 inference(modus_ponens,[status(thm)],[385, 384])).
% 3.92/2.76 tff(387,plain,
% 3.92/2.76 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 3.92/2.76 inference(modus_ponens,[status(thm)],[386, 382])).
% 3.92/2.76 tff(388,plain,(
% 3.92/2.76 ![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 3.92/2.76 inference(skolemize,[status(sab)],[387])).
% 3.92/2.76 tff(389,plain,
% 3.92/2.76 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 3.92/2.76 inference(modus_ponens,[status(thm)],[388, 381])).
% 3.92/2.76 tff(390,plain,
% 3.92/2.76 (((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))) <=> ((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 3.92/2.76 inference(rewrite,[status(thm)],[])).
% 3.92/2.76 tff(391,plain,
% 3.92/2.76 ((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 3.92/2.76 inference(quant_inst,[status(thm)],[])).
% 3.92/2.76 tff(392,plain,
% 3.92/2.76 ((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 3.92/2.76 inference(modus_ponens,[status(thm)],[391, 390])).
% 3.92/2.76 tff(393,plain,
% 3.92/2.76 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[392, 389])).
% 3.92/2.76 tff(394,plain,
% 3.92/2.76 (iLEQ(suc(z), suc(z))),
% 3.92/2.76 inference(unit_resolution,[status(thm)],[393, 379, 378])).
% 3.92/2.76 tff(395,plain,
% 3.92/2.76 (^[B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : refl(((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))),
% 3.92/2.76 inference(bind,[status(th)],[])).
% 3.92/2.76 tff(396,plain,
% 3.92/2.76 (![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) <=> ![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 3.92/2.76 inference(quant_intro,[status(thm)],[395])).
% 3.92/2.76 tff(397,plain,
% 3.92/2.76 (![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) <=> ![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 3.92/2.77 inference(rewrite,[status(thm)],[])).
% 3.92/2.77 tff(398,plain,
% 3.92/2.77 (^[B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_311)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) <=> ((~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) <=> ((~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) <=> (((~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_310)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_312)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_312)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_313)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(B_311), suc(B_312)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(B_311), suc(B_312)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(B_310), suc(B_311)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(B_310), suc(B_311)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(A_4), suc(B_310)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(A_4), suc(B_310)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~iLEQ(suc(B_312), suc(B_313)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(B_312), suc(B_313)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(B_312), suc(B_313)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~iLEQ(suc(B_312), suc(B_313)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~iLEQ(suc(B_312), suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(A_4)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~iLEQ(suc(B_312), suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))))),
% 3.92/2.77 inference(bind,[status(th)],[])).
% 3.92/2.77 tff(399,plain,
% 3.92/2.77 (![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~iLEQ(suc(B_312), suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 3.92/2.77 inference(quant_intro,[status(thm)],[398])).
% 3.92/2.77 tff(400,axiom,(![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~iLEQ(suc(B_312), suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(A_4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_442')).
% 3.92/2.77 tff(401,plain,
% 3.92/2.77 (![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 3.92/2.77 inference(modus_ponens,[status(thm)],[400, 399])).
% 3.92/2.77 tff(402,plain,
% 3.92/2.77 (![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 3.92/2.77 inference(modus_ponens,[status(thm)],[401, 397])).
% 3.92/2.77 tff(403,plain,(
% 3.92/2.77 ![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 3.92/2.77 inference(skolemize,[status(sab)],[402])).
% 3.92/2.77 tff(404,plain,
% 3.92/2.77 (![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 3.92/2.77 inference(modus_ponens,[status(thm)],[403, 396])).
% 3.92/2.77 tff(405,plain,
% 3.92/2.77 (((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.92/2.77 inference(rewrite,[status(thm)],[])).
% 3.92/2.77 tff(406,plain,
% 3.92/2.77 (((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.92/2.77 inference(rewrite,[status(thm)],[])).
% 3.92/2.77 tff(407,plain,
% 3.92/2.77 (((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 3.92/2.77 inference(monotonicity,[status(thm)],[406])).
% 3.92/2.77 tff(408,plain,
% 3.92/2.77 (((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.92/2.78 inference(transitivity,[status(thm)],[407, 405])).
% 3.92/2.78 tff(409,plain,
% 3.92/2.78 ((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 3.92/2.78 inference(quant_inst,[status(thm)],[])).
% 3.92/2.78 tff(410,plain,
% 3.92/2.78 ((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 3.92/2.78 inference(modus_ponens,[status(thm)],[409, 408])).
% 3.92/2.78 tff(411,plain,
% 3.92/2.78 ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[410, 404])).
% 3.92/2.78 tff(412,plain,
% 3.92/2.78 ($false),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[411, 394, 379, 378])).
% 3.92/2.78 tff(413,plain,((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.78 tff(414,plain,
% 3.92/2.78 ($false),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[413, 377, 207])).
% 3.92/2.78 tff(415,plain,(tptp_fun__E_(s(s(|'0'|)), f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.78 tff(416,assumption,(tptp_fun__E_(s(s(|'0'|)), f(suc(z)))), introduced(assumption)).
% 3.92/2.78 tff(417,assumption,(tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))), introduced(assumption)).
% 3.92/2.78 tff(418,plain,
% 3.92/2.78 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))),
% 3.92/2.78 inference(rewrite,[status(thm)],[])).
% 3.92/2.78 tff(419,plain,
% 3.92/2.78 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))),
% 3.92/2.78 inference(rewrite,[status(thm)],[])).
% 3.92/2.78 tff(420,plain,
% 3.92/2.78 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))))),
% 3.92/2.78 inference(monotonicity,[status(thm)],[419])).
% 3.92/2.78 tff(421,plain,
% 3.92/2.78 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))),
% 3.92/2.78 inference(transitivity,[status(thm)],[420, 418])).
% 3.92/2.78 tff(422,plain,
% 3.92/2.78 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))),
% 3.92/2.78 inference(quant_inst,[status(thm)],[])).
% 3.92/2.78 tff(423,plain,
% 3.92/2.78 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))),
% 3.92/2.78 inference(modus_ponens,[status(thm)],[422, 421])).
% 3.92/2.78 tff(424,plain,
% 3.92/2.78 ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[423, 305])).
% 3.92/2.78 tff(425,plain,
% 3.92/2.78 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[424, 417, 416])).
% 3.92/2.78 tff(426,plain,
% 3.92/2.78 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.92/2.78 inference(rewrite,[status(thm)],[])).
% 3.92/2.78 tff(427,plain,
% 3.92/2.78 (((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.92/2.78 inference(rewrite,[status(thm)],[])).
% 3.92/2.78 tff(428,plain,
% 3.92/2.78 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 3.92/2.78 inference(monotonicity,[status(thm)],[427])).
% 3.92/2.78 tff(429,plain,
% 3.92/2.78 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.92/2.78 inference(transitivity,[status(thm)],[428, 426])).
% 3.92/2.78 tff(430,plain,
% 3.92/2.78 ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))),
% 3.92/2.78 inference(quant_inst,[status(thm)],[])).
% 3.92/2.78 tff(431,plain,
% 3.92/2.78 ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 3.92/2.78 inference(modus_ponens,[status(thm)],[430, 429])).
% 3.92/2.78 tff(432,plain,
% 3.92/2.78 ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[431, 323])).
% 3.92/2.78 tff(433,plain,
% 3.92/2.78 ($false),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[432, 425, 417, 416])).
% 3.92/2.78 tff(434,plain,((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.78 tff(435,plain,
% 3.92/2.78 (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[434, 415])).
% 3.92/2.78 tff(436,plain,
% 3.92/2.78 (((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))) <=> ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 3.92/2.78 inference(rewrite,[status(thm)],[])).
% 3.92/2.78 tff(437,plain,
% 3.92/2.78 ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 3.92/2.78 inference(quant_inst,[status(thm)],[])).
% 3.92/2.78 tff(438,plain,
% 3.92/2.78 ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 3.92/2.78 inference(modus_ponens,[status(thm)],[437, 436])).
% 3.92/2.78 tff(439,plain,
% 3.92/2.78 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[438, 91])).
% 3.92/2.78 tff(440,plain,
% 3.92/2.78 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[439, 249])).
% 3.92/2.78 tff(441,plain,
% 3.92/2.78 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[440, 435])).
% 3.92/2.78 tff(442,plain,
% 3.92/2.78 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[358, 441])).
% 3.92/2.78 tff(443,plain,
% 3.92/2.78 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[376, 442])).
% 3.92/2.78 tff(444,plain,
% 3.92/2.78 (~tptp_fun__E_(|'0'|, f(z))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[413, 443])).
% 3.92/2.78 tff(445,plain,
% 3.92/2.78 (~tptp_fun__LE_(f(z), s(|'0'|))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[206, 444])).
% 3.92/2.78 tff(446,plain,
% 3.92/2.78 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[150, 445, 441])).
% 3.92/2.78 tff(447,assumption,(tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 3.92/2.78 tff(448,assumption,(~iLEQ(suc(z), suc(z))), introduced(assumption)).
% 3.92/2.78 tff(449,plain,
% 3.92/2.78 (~tptp_fun__E_(s(|'0'|), f(z))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[165, 448, 447])).
% 3.92/2.78 tff(450,assumption,(~tptp_fun__LE_(f(z), s(s(s(|'0'|))))), introduced(assumption)).
% 3.92/2.78 tff(451,plain,
% 3.92/2.78 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))),
% 3.92/2.78 inference(quant_inst,[status(thm)],[])).
% 3.92/2.78 tff(452,plain,
% 3.92/2.78 (tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[451, 9])).
% 3.92/2.78 tff(453,plain,
% 3.92/2.78 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(z)))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(z)))),
% 3.92/2.78 inference(rewrite,[status(thm)],[])).
% 3.92/2.78 tff(454,plain,
% 3.92/2.78 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(z)))),
% 3.92/2.78 inference(quant_inst,[status(thm)],[])).
% 3.92/2.78 tff(455,plain,
% 3.92/2.78 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(z))),
% 3.92/2.78 inference(modus_ponens,[status(thm)],[454, 453])).
% 3.92/2.78 tff(456,plain,
% 3.92/2.78 (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(z))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[455, 39])).
% 3.92/2.78 tff(457,plain,
% 3.92/2.78 (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(z))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[456, 452])).
% 3.92/2.78 tff(458,plain,
% 3.92/2.78 (tptp_fun__E_(s(s(s(|'0'|))), f(z))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[457, 450])).
% 3.92/2.78 tff(459,plain,
% 3.92/2.78 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))),
% 3.92/2.78 inference(rewrite,[status(thm)],[])).
% 3.92/2.78 tff(460,plain,
% 3.92/2.78 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))),
% 3.92/2.78 inference(quant_inst,[status(thm)],[])).
% 3.92/2.78 tff(461,plain,
% 3.92/2.78 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 3.92/2.78 inference(modus_ponens,[status(thm)],[460, 459])).
% 3.92/2.78 tff(462,plain,
% 3.92/2.78 (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[461, 22])).
% 3.92/2.78 tff(463,plain,
% 3.92/2.78 (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[462, 29])).
% 3.92/2.78 tff(464,plain,
% 3.92/2.78 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[463, 450])).
% 3.92/2.78 tff(465,plain,
% 3.92/2.78 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))))),
% 3.92/2.78 inference(rewrite,[status(thm)],[])).
% 3.92/2.78 tff(466,plain,
% 3.92/2.78 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))))),
% 3.92/2.78 inference(quant_inst,[status(thm)],[])).
% 3.92/2.78 tff(467,plain,
% 3.92/2.78 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z)))),
% 3.92/2.78 inference(modus_ponens,[status(thm)],[466, 465])).
% 3.92/2.78 tff(468,plain,
% 3.92/2.78 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z)))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[467, 54])).
% 3.92/2.78 tff(469,plain,
% 3.92/2.78 ($false),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[468, 464, 458, 448])).
% 3.92/2.78 tff(470,plain,(tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | iLEQ(suc(z), suc(z))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.78 tff(471,plain,
% 3.92/2.78 (tptp_fun__LE_(f(z), s(s(s(|'0'|))))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[470, 448])).
% 3.92/2.78 tff(472,plain,
% 3.92/2.78 (tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[185, 2])).
% 3.92/2.78 tff(473,plain,
% 3.92/2.78 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 3.92/2.78 inference(rewrite,[status(thm)],[])).
% 3.92/2.78 tff(474,plain,
% 3.92/2.78 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 3.92/2.78 inference(quant_inst,[status(thm)],[])).
% 3.92/2.78 tff(475,plain,
% 3.92/2.78 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 3.92/2.78 inference(modus_ponens,[status(thm)],[474, 473])).
% 3.92/2.78 tff(476,plain,
% 3.92/2.78 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[475, 305])).
% 3.92/2.78 tff(477,plain,
% 3.92/2.78 (~tptp_fun__E_(s(s(|'0'|)), f(z))),
% 3.92/2.78 inference(unit_resolution,[status(thm)],[476, 448, 472])).
% 3.92/2.78 tff(478,plain,
% 3.92/2.78 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z)))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 3.92/2.78 inference(rewrite,[status(thm)],[])).
% 3.92/2.78 tff(479,plain,
% 3.92/2.78 (((~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z))) <=> (tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 3.92/2.78 inference(rewrite,[status(thm)],[])).
% 3.92/2.78 tff(480,plain,
% 3.92/2.78 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 3.92/2.78 inference(monotonicity,[status(thm)],[479])).
% 3.92/2.78 tff(481,plain,
% 3.92/2.78 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 3.92/2.78 inference(transitivity,[status(thm)],[480, 478])).
% 3.92/2.78 tff(482,plain,
% 3.92/2.78 ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 3.92/2.78 inference(quant_inst,[status(thm)],[])).
% 3.92/2.78 tff(483,plain,
% 3.92/2.78 ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z))),
% 3.92/2.79 inference(modus_ponens,[status(thm)],[482, 481])).
% 3.92/2.79 tff(484,plain,
% 3.92/2.79 (tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z))),
% 3.92/2.79 inference(unit_resolution,[status(thm)],[483, 125])).
% 3.92/2.79 tff(485,plain,
% 3.92/2.79 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 3.92/2.79 inference(unit_resolution,[status(thm)],[484, 477, 471])).
% 3.92/2.79 tff(486,plain,
% 3.92/2.79 ($false),
% 3.92/2.79 inference(unit_resolution,[status(thm)],[114, 485, 449, 2])).
% 3.92/2.79 tff(487,plain,(iLEQ(suc(z), suc(z)) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.79 tff(488,plain,
% 3.92/2.79 (iLEQ(suc(z), suc(z))),
% 3.92/2.79 inference(unit_resolution,[status(thm)],[487, 446, 445])).
% 3.92/2.79 tff(489,plain,
% 3.92/2.79 (~tptp_fun__E_(s(|'0'|), f(z))),
% 3.92/2.79 inference(unit_resolution,[status(thm)],[183, 488, 446])).
% 3.92/2.79 tff(490,plain,
% 3.92/2.79 (~tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 3.92/2.79 inference(unit_resolution,[status(thm)],[114, 489, 445])).
% 3.92/2.79 tff(491,plain,
% 3.92/2.79 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.92/2.79 inference(rewrite,[status(thm)],[])).
% 3.92/2.79 tff(492,plain,
% 3.92/2.79 (((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.92/2.79 inference(rewrite,[status(thm)],[])).
% 3.92/2.79 tff(493,plain,
% 3.92/2.79 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 3.92/2.79 inference(monotonicity,[status(thm)],[492])).
% 3.92/2.79 tff(494,plain,
% 3.92/2.79 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.92/2.79 inference(transitivity,[status(thm)],[493, 491])).
% 3.92/2.79 tff(495,plain,
% 3.92/2.79 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))))),
% 3.92/2.79 inference(quant_inst,[status(thm)],[])).
% 3.92/2.79 tff(496,plain,
% 3.92/2.79 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 3.92/2.79 inference(modus_ponens,[status(thm)],[495, 494])).
% 3.92/2.79 tff(497,plain,
% 3.92/2.79 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 3.92/2.79 inference(unit_resolution,[status(thm)],[496, 72])).
% 3.92/2.79 tff(498,plain,
% 3.92/2.79 ($false),
% 3.92/2.79 inference(unit_resolution,[status(thm)],[497, 464, 458, 488])).
% 3.92/2.79 tff(499,plain,(tptp_fun__LE_(f(z), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 3.92/2.79 tff(500,plain,
% 3.92/2.79 (tptp_fun__E_(s(s(|'0'|)), f(z))),
% 3.92/2.79 inference(unit_resolution,[status(thm)],[484, 499, 490])).
% 3.92/2.79 tff(501,plain,
% 3.92/2.79 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.92/2.79 inference(rewrite,[status(thm)],[])).
% 3.92/2.79 tff(502,plain,
% 3.92/2.79 (((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.92/2.79 inference(rewrite,[status(thm)],[])).
% 3.92/2.79 tff(503,plain,
% 3.92/2.79 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 3.92/2.79 inference(monotonicity,[status(thm)],[502])).
% 3.92/2.79 tff(504,plain,
% 3.92/2.79 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.92/2.79 inference(transitivity,[status(thm)],[503, 501])).
% 3.92/2.79 tff(505,plain,
% 3.92/2.79 ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))),
% 3.92/2.79 inference(quant_inst,[status(thm)],[])).
% 3.92/2.79 tff(506,plain,
% 3.92/2.79 ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 3.92/2.79 inference(modus_ponens,[status(thm)],[505, 504])).
% 3.92/2.79 tff(507,plain,
% 3.92/2.79 ($false),
% 3.92/2.79 inference(unit_resolution,[status(thm)],[506, 323, 500, 415, 488])).
% 3.92/2.79 % SZS output end Proof
%------------------------------------------------------------------------------