TSTP Solution File: SYO674-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO674-1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 01:41:17 EDT 2022
% Result : Unsatisfiable 3.45s 2.46s
% Output : Proof 3.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SYO674-1 : TPTP v8.1.0. Released v7.3.0.
% 0.09/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.30 % Computer : n013.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Mon Sep 5 15:43:47 EDT 2022
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.30 Usage: tptp [options] [-file:]file
% 0.11/0.30 -h, -? prints this message.
% 0.11/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.30 -m, -model generate model.
% 0.11/0.30 -p, -proof generate proof.
% 0.11/0.30 -c, -core generate unsat core of named formulas.
% 0.11/0.30 -st, -statistics display statistics.
% 0.11/0.30 -t:timeout set timeout (in second).
% 0.11/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.30 -<param>:<value> configuration parameter and value.
% 0.11/0.30 -o:<output-file> file to place output in.
% 3.45/2.46 % SZS status Unsatisfiable
% 3.45/2.46 % SZS output start Proof
% 3.45/2.46 tff(iLEQ_type, type, (
% 3.45/2.46 iLEQ: ( $i * $i ) > $o)).
% 3.45/2.46 tff(suc_type, type, (
% 3.45/2.46 suc: $i > $i)).
% 3.45/2.46 tff(z_type, type, (
% 3.45/2.46 z: $i)).
% 3.45/2.46 tff(tptp_fun__E__type, type, (
% 3.45/2.46 tptp_fun__E_: ( $i * $i ) > $o)).
% 3.45/2.46 tff(f_type, type, (
% 3.45/2.46 f: $i > $i)).
% 3.45/2.46 tff(tptp_fun__0__type, type, (
% 3.45/2.46 tptp_fun__0_: $i)).
% 3.45/2.46 tff(tptp_fun__LE__type, type, (
% 3.45/2.46 tptp_fun__LE_: ( $i * $i ) > $o)).
% 3.45/2.46 tff(s_type, type, (
% 3.45/2.46 s: $i > $i)).
% 3.45/2.46 tff(1,assumption,(~iLEQ(suc(z), suc(z))), introduced(assumption)).
% 3.45/2.46 tff(2,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 3.45/2.46 tff(3,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), introduced(assumption)).
% 3.45/2.46 tff(4,plain,
% 3.45/2.46 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(s(s(|'0'|)))) <=> tptp_fun__LE_(f(A), s(s(s(|'0'|)))))),
% 3.45/2.46 inference(bind,[status(th)],[])).
% 3.45/2.46 tff(5,plain,
% 3.45/2.46 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|)))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))),
% 3.45/2.46 inference(quant_intro,[status(thm)],[4])).
% 3.45/2.46 tff(6,plain,
% 3.45/2.46 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|)))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))),
% 3.45/2.46 inference(rewrite,[status(thm)],[])).
% 3.45/2.46 tff(7,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_498')).
% 3.45/2.46 tff(8,plain,
% 3.45/2.46 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))),
% 3.45/2.46 inference(modus_ponens,[status(thm)],[7, 6])).
% 3.45/2.46 tff(9,plain,(
% 3.45/2.46 ![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))),
% 3.45/2.46 inference(skolemize,[status(sab)],[8])).
% 3.45/2.46 tff(10,plain,
% 3.45/2.46 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))),
% 3.45/2.46 inference(modus_ponens,[status(thm)],[9, 5])).
% 3.45/2.46 tff(11,plain,
% 3.45/2.46 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))),
% 3.45/2.46 inference(quant_inst,[status(thm)],[])).
% 3.45/2.46 tff(12,plain,
% 3.45/2.46 ($false),
% 3.45/2.46 inference(unit_resolution,[status(thm)],[11, 10, 3])).
% 3.45/2.46 tff(13,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 3.45/2.46 tff(14,plain,
% 3.45/2.46 (^[B_158: $i] : refl((tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|)))))) <=> (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|)))))))),
% 3.45/2.46 inference(bind,[status(th)],[])).
% 3.45/2.46 tff(15,plain,
% 3.45/2.46 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|)))))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 3.45/2.46 inference(quant_intro,[status(thm)],[14])).
% 3.45/2.46 tff(16,plain,
% 3.45/2.46 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|)))))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 3.45/2.46 inference(rewrite,[status(thm)],[])).
% 3.45/2.46 tff(17,plain,
% 3.45/2.46 (^[B_158: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158)))) | tptp_fun__LE_(f(B_158), s(s(|'0'|)))) <=> (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|)))))))),
% 3.45/2.46 inference(bind,[status(th)],[])).
% 3.45/2.46 tff(18,plain,
% 3.45/2.46 (![B_158: $i] : (((~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158)))) | tptp_fun__LE_(f(B_158), s(s(|'0'|)))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 3.45/2.46 inference(quant_intro,[status(thm)],[17])).
% 3.45/2.46 tff(19,axiom,(![B_158: $i] : (((~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158)))) | tptp_fun__LE_(f(B_158), s(s(|'0'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_129')).
% 3.45/2.46 tff(20,plain,
% 3.45/2.46 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 3.45/2.47 inference(modus_ponens,[status(thm)],[19, 18])).
% 3.45/2.47 tff(21,plain,
% 3.45/2.47 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 3.45/2.47 inference(modus_ponens,[status(thm)],[20, 16])).
% 3.45/2.47 tff(22,plain,(
% 3.45/2.47 ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 3.45/2.47 inference(skolemize,[status(sab)],[21])).
% 3.45/2.47 tff(23,plain,
% 3.45/2.47 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 3.45/2.47 inference(modus_ponens,[status(thm)],[22, 15])).
% 3.45/2.47 tff(24,plain,
% 3.45/2.47 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), 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_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), 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'|))))))),
% 3.45/2.47 inference(rewrite,[status(thm)],[])).
% 3.45/2.47 tff(25,plain,
% 3.45/2.47 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), 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'|))))))),
% 3.45/2.47 inference(quant_inst,[status(thm)],[])).
% 3.45/2.47 tff(26,plain,
% 3.45/2.47 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), 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'|)))))),
% 3.45/2.47 inference(modus_ponens,[status(thm)],[25, 24])).
% 3.45/2.47 tff(27,plain,
% 3.45/2.47 (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'|)))))),
% 3.45/2.47 inference(unit_resolution,[status(thm)],[26, 23])).
% 3.45/2.47 tff(28,plain,
% 3.45/2.47 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 3.45/2.47 inference(unit_resolution,[status(thm)],[27, 13])).
% 3.45/2.47 tff(29,plain,
% 3.45/2.47 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 3.45/2.47 inference(unit_resolution,[status(thm)],[28, 2])).
% 3.45/2.47 tff(30,plain,
% 3.45/2.47 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 3.45/2.47 inference(quant_inst,[status(thm)],[])).
% 3.45/2.47 tff(31,plain,
% 3.45/2.47 (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 3.45/2.47 inference(unit_resolution,[status(thm)],[30, 10])).
% 3.45/2.47 tff(32,plain,
% 3.45/2.47 (^[B_158: $i] : refl((tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))))) <=> (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))))))),
% 3.45/2.47 inference(bind,[status(th)],[])).
% 3.45/2.47 tff(33,plain,
% 3.45/2.47 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(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(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 3.45/2.47 inference(quant_intro,[status(thm)],[32])).
% 3.45/2.47 tff(34,plain,
% 3.45/2.47 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(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(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 3.45/2.47 inference(rewrite,[status(thm)],[])).
% 3.45/2.47 tff(35,plain,
% 3.45/2.47 (^[B_158: $i] : rewrite((((~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_158))) | tptp_fun__LE_(f(B_158), s(s(|'0'|)))) <=> (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))))))),
% 3.45/2.47 inference(bind,[status(th)],[])).
% 3.45/2.47 tff(36,plain,
% 3.45/2.47 (![B_158: $i] : (((~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_158))) | tptp_fun__LE_(f(B_158), s(s(|'0'|)))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 3.45/2.47 inference(quant_intro,[status(thm)],[35])).
% 3.45/2.47 tff(37,axiom,(![B_158: $i] : (((~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_158))) | tptp_fun__LE_(f(B_158), s(s(|'0'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_139')).
% 3.45/2.47 tff(38,plain,
% 3.45/2.47 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 3.45/2.47 inference(modus_ponens,[status(thm)],[37, 36])).
% 3.45/2.47 tff(39,plain,
% 3.45/2.47 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 3.45/2.47 inference(modus_ponens,[status(thm)],[38, 34])).
% 3.45/2.47 tff(40,plain,(
% 3.45/2.47 ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 3.45/2.47 inference(skolemize,[status(sab)],[39])).
% 3.45/2.47 tff(41,plain,
% 3.45/2.47 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 3.45/2.47 inference(modus_ponens,[status(thm)],[40, 33])).
% 3.45/2.47 tff(42,plain,
% 3.45/2.47 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), 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(s(|'0'|))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), 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(s(|'0'|))))))),
% 3.45/2.47 inference(rewrite,[status(thm)],[])).
% 3.45/2.47 tff(43,plain,
% 3.45/2.47 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), 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(s(|'0'|))))))),
% 3.45/2.47 inference(quant_inst,[status(thm)],[])).
% 3.45/2.47 tff(44,plain,
% 3.45/2.47 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), 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(s(|'0'|)))))),
% 3.45/2.47 inference(modus_ponens,[status(thm)],[43, 42])).
% 3.45/2.47 tff(45,plain,
% 3.45/2.47 (tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 3.45/2.47 inference(unit_resolution,[status(thm)],[44, 41, 2, 31])).
% 3.45/2.47 tff(46,plain,
% 3.45/2.47 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))),
% 3.45/2.47 inference(bind,[status(th)],[])).
% 3.45/2.47 tff(47,plain,
% 3.45/2.47 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.47 inference(quant_intro,[status(thm)],[46])).
% 3.45/2.47 tff(48,plain,
% 3.45/2.47 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.47 inference(rewrite,[status(thm)],[])).
% 3.45/2.47 tff(49,plain,
% 3.45/2.47 (^[A_1: $i] : rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(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(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))),
% 3.45/2.47 inference(bind,[status(th)],[])).
% 3.45/2.47 tff(50,plain,
% 3.45/2.47 (![A_1: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(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(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.47 inference(quant_intro,[status(thm)],[49])).
% 3.45/2.47 tff(51,axiom,(![A_1: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_126')).
% 3.45/2.47 tff(52,plain,
% 3.45/2.47 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 3.45/2.47 tff(53,plain,
% 3.45/2.47 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.47 inference(modus_ponens,[status(thm)],[52, 48])).
% 3.45/2.47 tff(54,plain,(
% 3.45/2.47 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.47 inference(skolemize,[status(sab)],[53])).
% 3.45/2.47 tff(55,plain,
% 3.45/2.47 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.47 inference(modus_ponens,[status(thm)],[54, 47])).
% 3.45/2.47 tff(56,plain,
% 3.45/2.47 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~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))))))),
% 3.45/2.47 inference(rewrite,[status(thm)],[])).
% 3.45/2.47 tff(57,plain,
% 3.45/2.47 ((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))))))),
% 3.45/2.47 inference(rewrite,[status(thm)],[])).
% 3.45/2.47 tff(58,plain,
% 3.45/2.47 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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)))))))),
% 3.45/2.47 inference(monotonicity,[status(thm)],[57])).
% 3.45/2.47 tff(59,plain,
% 3.45/2.47 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~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))))))),
% 3.45/2.47 inference(transitivity,[status(thm)],[58, 56])).
% 3.45/2.47 tff(60,plain,
% 3.45/2.47 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (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)))))),
% 3.45/2.47 inference(quant_inst,[status(thm)],[])).
% 3.45/2.47 tff(61,plain,
% 3.45/2.47 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~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)))))),
% 3.45/2.47 inference(modus_ponens,[status(thm)],[60, 59])).
% 3.45/2.47 tff(62,plain,
% 3.45/2.47 ((~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)))))),
% 3.45/2.47 inference(unit_resolution,[status(thm)],[61, 55])).
% 3.45/2.47 tff(63,plain,
% 3.45/2.47 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 3.45/2.47 inference(unit_resolution,[status(thm)],[62, 45, 29])).
% 3.45/2.47 tff(64,plain,
% 3.45/2.47 (^[B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : refl(((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))),
% 3.45/2.47 inference(bind,[status(th)],[])).
% 3.45/2.47 tff(65,plain,
% 3.45/2.47 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) <=> ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.47 inference(quant_intro,[status(thm)],[64])).
% 3.45/2.47 tff(66,plain,
% 3.45/2.47 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) <=> ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.47 inference(rewrite,[status(thm)],[])).
% 3.45/2.47 tff(67,plain,
% 3.45/2.47 (^[B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $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(trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_160), suc(B_161)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_160), suc(B_161)))) <=> ((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) <=> ((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) <=> (((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))))), rewrite((((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), (((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), (((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_159), suc(B_160)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_159), suc(B_160)))) <=> ((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) <=> ((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) <=> (((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))))), rewrite((((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), (((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), (((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_161), suc(B_162)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_161), suc(B_162)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), (((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), (((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) | (~iLEQ(suc(B_162), suc(B_163)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_162), suc(B_163)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_162), suc(B_163)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) | (~iLEQ(suc(B_162), suc(B_163)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) | (~iLEQ(suc(B_162), suc(B_163)))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(A_1), suc(B_159)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) | (~iLEQ(suc(B_162), suc(B_163)))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))))),
% 3.45/2.48 inference(bind,[status(th)],[])).
% 3.45/2.48 tff(68,plain,
% 3.45/2.48 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : (((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) | (~iLEQ(suc(B_162), suc(B_163)))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.48 inference(quant_intro,[status(thm)],[67])).
% 3.45/2.48 tff(69,axiom,(![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : (((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) | (~iLEQ(suc(B_162), suc(B_163)))) | (~iLEQ(suc(A_1), suc(B_159))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_431')).
% 3.45/2.48 tff(70,plain,
% 3.45/2.48 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.48 inference(modus_ponens,[status(thm)],[69, 68])).
% 3.45/2.48 tff(71,plain,
% 3.45/2.48 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.48 inference(modus_ponens,[status(thm)],[70, 66])).
% 3.45/2.48 tff(72,plain,(
% 3.45/2.48 ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.48 inference(skolemize,[status(sab)],[71])).
% 3.45/2.48 tff(73,plain,
% 3.45/2.48 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 3.45/2.48 inference(modus_ponens,[status(thm)],[72, 65])).
% 3.45/2.48 tff(74,plain,
% 3.45/2.48 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~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)))))),
% 3.45/2.48 inference(rewrite,[status(thm)],[])).
% 3.45/2.48 tff(75,plain,
% 3.45/2.48 (((~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)))) | (~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(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))))) | (~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)))) | (~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(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.45/2.48 inference(rewrite,[status(thm)],[])).
% 3.45/2.48 tff(76,plain,
% 3.45/2.48 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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)))) | (~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(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))))) | (~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)))) | (~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)))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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))))))),
% 3.45/2.49 inference(monotonicity,[status(thm)],[75])).
% 3.45/2.49 tff(77,plain,
% 3.45/2.49 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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)))) | (~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(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))))) | (~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)))) | (~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)))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~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)))))),
% 3.45/2.49 inference(transitivity,[status(thm)],[76, 74])).
% 3.45/2.49 tff(78,plain,
% 3.45/2.49 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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)))) | (~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(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))))) | (~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)))) | (~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)))))),
% 3.45/2.49 inference(quant_inst,[status(thm)],[])).
% 3.45/2.49 tff(79,plain,
% 3.45/2.49 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[78, 77])).
% 3.45/2.49 tff(80,plain,
% 3.45/2.49 ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[79, 73])).
% 3.45/2.49 tff(81,plain,
% 3.45/2.49 ($false),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[80, 63, 45, 29])).
% 3.45/2.49 tff(82,plain,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 3.45/2.49 tff(83,assumption,(~tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 3.45/2.49 tff(84,plain,
% 3.45/2.49 (^[B_228: $i] : refl((tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))) <=> (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))))),
% 3.45/2.49 inference(bind,[status(th)],[])).
% 3.45/2.49 tff(85,plain,
% 3.45/2.49 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))) <=> ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 3.45/2.49 inference(quant_intro,[status(thm)],[84])).
% 3.45/2.49 tff(86,plain,
% 3.45/2.49 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))) <=> ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(87,plain,
% 3.45/2.49 (^[B_228: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))) | tptp_fun__LE_(f(B_228), s(|'0'|))) <=> (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))))),
% 3.45/2.49 inference(bind,[status(th)],[])).
% 3.45/2.49 tff(88,plain,
% 3.45/2.49 (![B_228: $i] : (((~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))) | tptp_fun__LE_(f(B_228), s(|'0'|))) <=> ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 3.45/2.49 inference(quant_intro,[status(thm)],[87])).
% 3.45/2.49 tff(89,axiom,(![B_228: $i] : (((~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))) | tptp_fun__LE_(f(B_228), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_84')).
% 3.45/2.49 tff(90,plain,
% 3.45/2.49 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[89, 88])).
% 3.45/2.49 tff(91,plain,
% 3.45/2.49 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[90, 86])).
% 3.45/2.49 tff(92,plain,(
% 3.45/2.49 ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 3.45/2.49 inference(skolemize,[status(sab)],[91])).
% 3.45/2.49 tff(93,plain,
% 3.45/2.49 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[92, 85])).
% 3.45/2.49 tff(94,plain,
% 3.45/2.49 (((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(95,plain,
% 3.45/2.49 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 3.45/2.49 inference(quant_inst,[status(thm)],[])).
% 3.45/2.49 tff(96,plain,
% 3.45/2.49 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[95, 94])).
% 3.45/2.49 tff(97,plain,
% 3.45/2.49 (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[96, 93])).
% 3.45/2.49 tff(98,plain,
% 3.45/2.49 (tptp_fun__LE_(f(z), s(|'0'|))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[97, 83, 82])).
% 3.45/2.49 tff(99,plain,
% 3.45/2.49 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(100,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_204')).
% 3.45/2.49 tff(101,plain,
% 3.45/2.49 (~tptp_fun__LE_(f(z), |'0'|)),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[100, 99])).
% 3.45/2.49 tff(102,plain,
% 3.45/2.49 (^[B_253: $i] : refl(((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253))) <=> ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253))))),
% 3.45/2.49 inference(bind,[status(th)],[])).
% 3.45/2.49 tff(103,plain,
% 3.45/2.49 (![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253))) <=> ![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 3.45/2.49 inference(quant_intro,[status(thm)],[102])).
% 3.45/2.49 tff(104,plain,
% 3.45/2.49 (![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253))) <=> ![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(105,plain,
% 3.45/2.49 (^[B_253: $i] : rewrite((((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_253))) | tptp_fun__LE_(f(B_253), |'0'|)) <=> ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253))))),
% 3.45/2.49 inference(bind,[status(th)],[])).
% 3.45/2.49 tff(106,plain,
% 3.45/2.49 (![B_253: $i] : (((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_253))) | tptp_fun__LE_(f(B_253), |'0'|)) <=> ![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 3.45/2.49 inference(quant_intro,[status(thm)],[105])).
% 3.45/2.49 tff(107,axiom,(![B_253: $i] : (((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_253))) | tptp_fun__LE_(f(B_253), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_176')).
% 3.45/2.49 tff(108,plain,
% 3.45/2.49 (![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[107, 106])).
% 3.45/2.49 tff(109,plain,
% 3.45/2.49 (![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[108, 104])).
% 3.45/2.49 tff(110,plain,(
% 3.45/2.49 ![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 3.45/2.49 inference(skolemize,[status(sab)],[109])).
% 3.45/2.49 tff(111,plain,
% 3.45/2.49 (![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[110, 103])).
% 3.45/2.49 tff(112,plain,
% 3.45/2.49 (((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(113,plain,
% 3.45/2.49 (((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z))) <=> (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(114,plain,
% 3.45/2.49 (((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))))),
% 3.45/2.49 inference(monotonicity,[status(thm)],[113])).
% 3.45/2.49 tff(115,plain,
% 3.45/2.49 (((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 3.45/2.49 inference(transitivity,[status(thm)],[114, 112])).
% 3.45/2.49 tff(116,plain,
% 3.45/2.49 ((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))),
% 3.45/2.49 inference(quant_inst,[status(thm)],[])).
% 3.45/2.49 tff(117,plain,
% 3.45/2.49 ((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[116, 115])).
% 3.45/2.49 tff(118,plain,
% 3.45/2.49 ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[117, 111, 101])).
% 3.45/2.49 tff(119,plain,
% 3.45/2.49 (tptp_fun__E_(|'0'|, f(z))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[118, 98])).
% 3.45/2.49 tff(120,plain,
% 3.45/2.49 (^[B_228: $i] : refl((tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))) <=> (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))))),
% 3.45/2.49 inference(bind,[status(th)],[])).
% 3.45/2.49 tff(121,plain,
% 3.45/2.49 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))) <=> ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 3.45/2.49 inference(quant_intro,[status(thm)],[120])).
% 3.45/2.49 tff(122,plain,
% 3.45/2.49 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))) <=> ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(123,plain,
% 3.45/2.49 (^[B_228: $i] : rewrite((((~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))) | tptp_fun__LE_(f(B_228), s(|'0'|))) <=> (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))))),
% 3.45/2.49 inference(bind,[status(th)],[])).
% 3.45/2.49 tff(124,plain,
% 3.45/2.49 (![B_228: $i] : (((~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))) | tptp_fun__LE_(f(B_228), s(|'0'|))) <=> ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 3.45/2.49 inference(quant_intro,[status(thm)],[123])).
% 3.45/2.49 tff(125,axiom,(![B_228: $i] : (((~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))) | tptp_fun__LE_(f(B_228), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_298')).
% 3.45/2.49 tff(126,plain,
% 3.45/2.49 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[125, 124])).
% 3.45/2.49 tff(127,plain,
% 3.45/2.49 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[126, 122])).
% 3.45/2.49 tff(128,plain,(
% 3.45/2.49 ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 3.45/2.49 inference(skolemize,[status(sab)],[127])).
% 3.45/2.49 tff(129,plain,
% 3.45/2.49 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[128, 121])).
% 3.45/2.49 tff(130,plain,
% 3.45/2.49 (((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(131,plain,
% 3.45/2.49 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 3.45/2.49 inference(quant_inst,[status(thm)],[])).
% 3.45/2.49 tff(132,plain,
% 3.45/2.49 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[131, 130])).
% 3.45/2.49 tff(133,plain,
% 3.45/2.49 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[132, 129, 82])).
% 3.45/2.49 tff(134,plain,
% 3.45/2.49 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[133, 83])).
% 3.45/2.49 tff(135,plain,
% 3.45/2.49 (^[B_253: $i] : refl((tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))) <=> (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))))),
% 3.45/2.49 inference(bind,[status(th)],[])).
% 3.45/2.49 tff(136,plain,
% 3.45/2.49 (![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))) <=> ![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 3.45/2.49 inference(quant_intro,[status(thm)],[135])).
% 3.45/2.49 tff(137,plain,
% 3.45/2.49 (![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))) <=> ![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(138,plain,
% 3.45/2.49 (^[B_253: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))) | tptp_fun__LE_(f(B_253), |'0'|)) <=> (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))))),
% 3.45/2.49 inference(bind,[status(th)],[])).
% 3.45/2.49 tff(139,plain,
% 3.45/2.49 (![B_253: $i] : (((~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))) | tptp_fun__LE_(f(B_253), |'0'|)) <=> ![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 3.45/2.49 inference(quant_intro,[status(thm)],[138])).
% 3.45/2.49 tff(140,axiom,(![B_253: $i] : (((~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))) | tptp_fun__LE_(f(B_253), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_50')).
% 3.45/2.49 tff(141,plain,
% 3.45/2.49 (![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[140, 139])).
% 3.45/2.49 tff(142,plain,
% 3.45/2.49 (![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[141, 137])).
% 3.45/2.49 tff(143,plain,(
% 3.45/2.49 ![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 3.45/2.49 inference(skolemize,[status(sab)],[142])).
% 3.45/2.49 tff(144,plain,
% 3.45/2.49 (![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[143, 136])).
% 3.45/2.49 tff(145,plain,
% 3.45/2.49 (((~![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(146,plain,
% 3.45/2.49 ((~![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 3.45/2.49 inference(quant_inst,[status(thm)],[])).
% 3.45/2.49 tff(147,plain,
% 3.45/2.49 ((~![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[146, 145])).
% 3.45/2.49 tff(148,plain,
% 3.45/2.49 ((~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[147, 101, 144])).
% 3.45/2.49 tff(149,plain,
% 3.45/2.49 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[148, 134])).
% 3.45/2.49 tff(150,plain,
% 3.45/2.49 (^[A_3: $i] : refl((iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))))),
% 3.45/2.49 inference(bind,[status(th)],[])).
% 3.45/2.49 tff(151,plain,
% 3.45/2.49 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 3.45/2.49 inference(quant_intro,[status(thm)],[150])).
% 3.45/2.49 tff(152,plain,
% 3.45/2.49 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(153,plain,
% 3.45/2.49 (^[A_3: $i] : rewrite((((~tptp_fun__E_(|'0'|, f(A_3))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | iLEQ(suc(A_3), suc(A_3))) <=> (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))))),
% 3.45/2.49 inference(bind,[status(th)],[])).
% 3.45/2.49 tff(154,plain,
% 3.45/2.49 (![A_3: $i] : (((~tptp_fun__E_(|'0'|, f(A_3))) | (~tptp_fun__E_(|'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_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 3.45/2.49 inference(quant_intro,[status(thm)],[153])).
% 3.45/2.49 tff(155,axiom,(![A_3: $i] : (((~tptp_fun__E_(|'0'|, f(A_3))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | iLEQ(suc(A_3), suc(A_3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_281')).
% 3.45/2.49 tff(156,plain,
% 3.45/2.49 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[155, 154])).
% 3.45/2.49 tff(157,plain,
% 3.45/2.49 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[156, 152])).
% 3.45/2.49 tff(158,plain,(
% 3.45/2.49 ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 3.45/2.49 inference(skolemize,[status(sab)],[157])).
% 3.45/2.49 tff(159,plain,
% 3.45/2.49 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[158, 151])).
% 3.45/2.49 tff(160,plain,
% 3.45/2.49 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))) <=> ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(161,plain,
% 3.45/2.49 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 3.45/2.49 inference(quant_inst,[status(thm)],[])).
% 3.45/2.49 tff(162,plain,
% 3.45/2.49 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[161, 160])).
% 3.45/2.49 tff(163,plain,
% 3.45/2.49 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[162, 159])).
% 3.45/2.49 tff(164,plain,
% 3.45/2.49 ($false),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[163, 149, 119, 1])).
% 3.45/2.49 tff(165,plain,(tptp_fun__E_(s(|'0'|), f(suc(z))) | iLEQ(suc(z), suc(z))), inference(lemma,lemma(discharge,[]))).
% 3.45/2.49 tff(166,plain,
% 3.45/2.49 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[165, 1])).
% 3.45/2.49 tff(167,plain,
% 3.45/2.49 (^[A_2: $i] : refl((iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))))),
% 3.45/2.49 inference(bind,[status(th)],[])).
% 3.45/2.49 tff(168,plain,
% 3.45/2.49 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 3.45/2.49 inference(quant_intro,[status(thm)],[167])).
% 3.45/2.49 tff(169,plain,
% 3.45/2.49 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(170,plain,
% 3.45/2.49 (^[A_2: $i] : rewrite((((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))))),
% 3.45/2.49 inference(bind,[status(th)],[])).
% 3.45/2.49 tff(171,plain,
% 3.45/2.49 (![A_2: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(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(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 3.45/2.49 inference(quant_intro,[status(thm)],[170])).
% 3.45/2.49 tff(172,axiom,(![A_2: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_493')).
% 3.45/2.49 tff(173,plain,
% 3.45/2.49 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[172, 171])).
% 3.45/2.49 tff(174,plain,
% 3.45/2.49 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[173, 169])).
% 3.45/2.49 tff(175,plain,(
% 3.45/2.49 ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 3.45/2.49 inference(skolemize,[status(sab)],[174])).
% 3.45/2.49 tff(176,plain,
% 3.45/2.49 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[175, 168])).
% 3.45/2.49 tff(177,plain,
% 3.45/2.49 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(178,plain,
% 3.45/2.49 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 3.45/2.49 inference(quant_inst,[status(thm)],[])).
% 3.45/2.49 tff(179,plain,
% 3.45/2.49 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 3.45/2.49 inference(modus_ponens,[status(thm)],[178, 177])).
% 3.45/2.49 tff(180,plain,
% 3.45/2.49 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[179, 176])).
% 3.45/2.49 tff(181,plain,
% 3.45/2.49 (~tptp_fun__E_(s(|'0'|), f(z))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[180, 166, 1])).
% 3.45/2.49 tff(182,assumption,(~tptp_fun__LE_(f(z), s(s(|'0'|)))), introduced(assumption)).
% 3.45/2.49 tff(183,plain,
% 3.45/2.49 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))) | tptp_fun__LE_(f(z), s(s(s(|'0'|))))),
% 3.45/2.49 inference(quant_inst,[status(thm)],[])).
% 3.45/2.49 tff(184,plain,
% 3.45/2.49 (tptp_fun__LE_(f(z), s(s(s(|'0'|))))),
% 3.45/2.49 inference(unit_resolution,[status(thm)],[183, 10])).
% 3.45/2.49 tff(185,plain,
% 3.45/2.49 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), 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(s(|'0'|))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), 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(s(|'0'|))))))),
% 3.45/2.49 inference(rewrite,[status(thm)],[])).
% 3.45/2.49 tff(186,plain,
% 3.45/2.49 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), 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(s(|'0'|))))))),
% 3.45/2.50 inference(quant_inst,[status(thm)],[])).
% 3.45/2.50 tff(187,plain,
% 3.45/2.50 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), 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(s(|'0'|)))))),
% 3.45/2.50 inference(modus_ponens,[status(thm)],[186, 185])).
% 3.45/2.50 tff(188,plain,
% 3.45/2.50 (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[187, 41, 184])).
% 3.45/2.50 tff(189,plain,
% 3.45/2.50 (tptp_fun__E_(s(s(|'0'|)), f(z))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[188, 182])).
% 3.45/2.50 tff(190,plain,
% 3.45/2.50 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), 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_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), 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'|))))))),
% 3.45/2.50 inference(rewrite,[status(thm)],[])).
% 3.45/2.50 tff(191,plain,
% 3.45/2.50 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), 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'|))))))),
% 3.45/2.50 inference(quant_inst,[status(thm)],[])).
% 3.45/2.50 tff(192,plain,
% 3.45/2.50 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), 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'|)))))),
% 3.45/2.50 inference(modus_ponens,[status(thm)],[191, 190])).
% 3.45/2.50 tff(193,plain,
% 3.45/2.50 (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'|)))))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[192, 23])).
% 3.45/2.50 tff(194,plain,
% 3.45/2.50 (tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[193, 182, 31])).
% 3.45/2.50 tff(195,plain,
% 3.45/2.50 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 3.45/2.50 inference(rewrite,[status(thm)],[])).
% 3.45/2.50 tff(196,plain,
% 3.45/2.50 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 3.45/2.50 inference(quant_inst,[status(thm)],[])).
% 3.45/2.50 tff(197,plain,
% 3.45/2.50 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 3.45/2.50 inference(modus_ponens,[status(thm)],[196, 195])).
% 3.45/2.50 tff(198,plain,
% 3.45/2.50 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[197, 55])).
% 3.45/2.50 tff(199,plain,
% 3.45/2.50 ($false),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[198, 194, 189, 1])).
% 3.45/2.50 tff(200,plain,(tptp_fun__LE_(f(z), s(s(|'0'|))) | iLEQ(suc(z), suc(z))), inference(lemma,lemma(discharge,[]))).
% 3.45/2.50 tff(201,plain,
% 3.45/2.50 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[200, 1])).
% 3.45/2.50 tff(202,plain,
% 3.45/2.50 (((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))) <=> ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 3.45/2.50 inference(rewrite,[status(thm)],[])).
% 3.45/2.50 tff(203,plain,
% 3.45/2.50 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 3.45/2.50 inference(quant_inst,[status(thm)],[])).
% 3.45/2.50 tff(204,plain,
% 3.45/2.50 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 3.45/2.50 inference(modus_ponens,[status(thm)],[203, 202])).
% 3.45/2.50 tff(205,plain,
% 3.45/2.50 (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[204, 129])).
% 3.45/2.50 tff(206,plain,
% 3.45/2.50 (tptp_fun__LE_(f(z), s(|'0'|))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[205, 201, 181])).
% 3.45/2.50 tff(207,plain,
% 3.45/2.50 (tptp_fun__E_(|'0'|, f(z))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[118, 206])).
% 3.45/2.50 tff(208,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), introduced(assumption)).
% 3.45/2.50 tff(209,plain,
% 3.45/2.50 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), 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(s(|'0'|))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), 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(s(|'0'|))))))),
% 3.45/2.50 inference(rewrite,[status(thm)],[])).
% 3.45/2.50 tff(210,plain,
% 3.45/2.50 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), 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(s(|'0'|))))))),
% 3.45/2.50 inference(quant_inst,[status(thm)],[])).
% 3.45/2.50 tff(211,plain,
% 3.45/2.50 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), 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(s(|'0'|)))))),
% 3.45/2.50 inference(modus_ponens,[status(thm)],[210, 209])).
% 3.45/2.50 tff(212,plain,
% 3.45/2.50 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[211, 41, 13])).
% 3.45/2.50 tff(213,plain,
% 3.45/2.50 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[212, 208])).
% 3.45/2.50 tff(214,assumption,(~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))), introduced(assumption)).
% 3.45/2.50 tff(215,plain,
% 3.45/2.50 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))),
% 3.45/2.50 inference(quant_inst,[status(thm)],[])).
% 3.45/2.50 tff(216,plain,
% 3.45/2.50 ($false),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[215, 10, 214])).
% 3.45/2.50 tff(217,plain,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 3.45/2.50 tff(218,plain,
% 3.45/2.50 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), 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_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), 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'|))))))),
% 3.45/2.50 inference(rewrite,[status(thm)],[])).
% 3.45/2.50 tff(219,plain,
% 3.45/2.50 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), 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'|))))))),
% 3.45/2.50 inference(quant_inst,[status(thm)],[])).
% 3.45/2.50 tff(220,plain,
% 3.45/2.50 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), 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'|)))))),
% 3.45/2.50 inference(modus_ponens,[status(thm)],[219, 218])).
% 3.45/2.50 tff(221,plain,
% 3.45/2.50 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[220, 23, 217])).
% 3.45/2.50 tff(222,plain,
% 3.45/2.50 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[221, 208])).
% 3.45/2.50 tff(223,plain,
% 3.45/2.50 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~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)))))))),
% 3.45/2.50 inference(rewrite,[status(thm)],[])).
% 3.45/2.50 tff(224,plain,
% 3.45/2.50 ((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)))))))),
% 3.45/2.50 inference(rewrite,[status(thm)],[])).
% 3.45/2.50 tff(225,plain,
% 3.45/2.50 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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))))))))),
% 3.45/2.50 inference(monotonicity,[status(thm)],[224])).
% 3.45/2.50 tff(226,plain,
% 3.45/2.50 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~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)))))))),
% 3.45/2.50 inference(transitivity,[status(thm)],[225, 223])).
% 3.45/2.50 tff(227,plain,
% 3.45/2.50 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (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))))))),
% 3.45/2.50 inference(quant_inst,[status(thm)],[])).
% 3.45/2.50 tff(228,plain,
% 3.45/2.50 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~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))))))),
% 3.45/2.50 inference(modus_ponens,[status(thm)],[227, 226])).
% 3.45/2.50 tff(229,plain,
% 3.45/2.50 ((~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))))))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[228, 55])).
% 3.45/2.50 tff(230,plain,
% 3.45/2.50 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[229, 222, 213])).
% 3.45/2.50 tff(231,plain,
% 3.45/2.50 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~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))))))),
% 3.45/2.50 inference(rewrite,[status(thm)],[])).
% 3.45/2.50 tff(232,plain,
% 3.45/2.50 (((~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))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(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)))))) | (~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))))) | (~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(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 3.45/2.50 inference(rewrite,[status(thm)],[])).
% 3.45/2.50 tff(233,plain,
% 3.45/2.50 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(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)))))) | (~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))))) | (~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))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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)))))))),
% 3.45/2.50 inference(monotonicity,[status(thm)],[232])).
% 3.45/2.50 tff(234,plain,
% 3.45/2.50 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(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)))))) | (~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))))) | (~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))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~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))))))),
% 3.45/2.50 inference(transitivity,[status(thm)],[233, 231])).
% 3.45/2.50 tff(235,plain,
% 3.45/2.50 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~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))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(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)))))) | (~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))))) | (~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))))))),
% 3.45/2.50 inference(quant_inst,[status(thm)],[])).
% 3.45/2.50 tff(236,plain,
% 3.45/2.50 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 3.45/2.50 inference(modus_ponens,[status(thm)],[235, 234])).
% 3.45/2.50 tff(237,plain,
% 3.45/2.50 ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[236, 73])).
% 3.45/2.50 tff(238,plain,
% 3.45/2.50 ($false),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[237, 230, 222, 213])).
% 3.45/2.50 tff(239,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 3.45/2.50 tff(240,assumption,(tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), introduced(assumption)).
% 3.45/2.50 tff(241,assumption,(~iLEQ(suc(suc(z)), suc(suc(z)))), introduced(assumption)).
% 3.45/2.50 tff(242,plain,
% 3.45/2.50 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | ((~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_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 3.45/2.50 inference(rewrite,[status(thm)],[])).
% 3.45/2.50 tff(243,plain,
% 3.45/2.50 ((iLEQ(suc(suc(z)), 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)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 3.45/2.50 inference(rewrite,[status(thm)],[])).
% 3.45/2.50 tff(244,plain,
% 3.45/2.50 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))))),
% 3.45/2.50 inference(monotonicity,[status(thm)],[243])).
% 3.45/2.50 tff(245,plain,
% 3.45/2.50 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 3.45/2.50 inference(transitivity,[status(thm)],[244, 242])).
% 3.45/2.50 tff(246,plain,
% 3.45/2.50 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 3.45/2.50 inference(quant_inst,[status(thm)],[])).
% 3.45/2.50 tff(247,plain,
% 3.45/2.50 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 3.45/2.50 inference(modus_ponens,[status(thm)],[246, 245])).
% 3.45/2.50 tff(248,plain,
% 3.45/2.50 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[247, 176])).
% 3.45/2.50 tff(249,plain,
% 3.45/2.50 (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[248, 166, 241])).
% 3.45/2.50 tff(250,plain,
% 3.45/2.50 (((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 3.45/2.50 inference(rewrite,[status(thm)],[])).
% 3.45/2.50 tff(251,plain,
% 3.45/2.50 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 3.45/2.50 inference(quant_inst,[status(thm)],[])).
% 3.45/2.50 tff(252,plain,
% 3.45/2.50 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 3.45/2.50 inference(modus_ponens,[status(thm)],[251, 250])).
% 3.45/2.50 tff(253,plain,
% 3.45/2.50 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[252, 93])).
% 3.45/2.50 tff(254,plain,
% 3.45/2.50 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[253, 249, 240])).
% 3.45/2.50 tff(255,plain,
% 3.45/2.50 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[148, 254])).
% 3.45/2.50 tff(256,assumption,(tptp_fun__LE_(f(z), s(s(|'0'|)))), introduced(assumption)).
% 3.45/2.50 tff(257,plain,
% 3.45/2.50 (tptp_fun__LE_(f(z), s(|'0'|))),
% 3.45/2.50 inference(unit_resolution,[status(thm)],[205, 181, 256])).
% 3.45/2.51 tff(258,plain,
% 3.45/2.51 (tptp_fun__E_(|'0'|, f(z))),
% 3.45/2.51 inference(unit_resolution,[status(thm)],[118, 257])).
% 3.45/2.51 tff(259,plain,
% 3.45/2.51 ($false),
% 3.45/2.51 inference(unit_resolution,[status(thm)],[163, 258, 255, 1])).
% 3.45/2.51 tff(260,plain,(iLEQ(suc(z), suc(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | iLEQ(suc(suc(z)), suc(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 3.45/2.51 tff(261,plain,
% 3.45/2.51 (iLEQ(suc(z), suc(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | iLEQ(suc(suc(z)), suc(suc(z)))),
% 3.45/2.51 inference(unit_resolution,[status(thm)],[260, 239])).
% 3.45/2.51 tff(262,plain,
% 3.45/2.51 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 3.45/2.51 inference(unit_resolution,[status(thm)],[261, 1, 201])).
% 3.45/2.51 tff(263,plain,
% 3.45/2.51 (^[B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : refl(((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) <=> ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))),
% 3.45/2.51 inference(bind,[status(th)],[])).
% 3.45/2.51 tff(264,plain,
% 3.45/2.51 (![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) <=> ![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 3.45/2.51 inference(quant_intro,[status(thm)],[263])).
% 3.45/2.51 tff(265,plain,
% 3.45/2.51 (![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) <=> ![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 3.58/2.51 inference(rewrite,[status(thm)],[])).
% 3.58/2.51 tff(266,plain,
% 3.58/2.51 (^[B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) <=> ((~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) <=> (((~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))))), rewrite((((~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(A_2), suc(B_229)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(A_2), suc(B_229)))) <=> ((~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) <=> ((~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) <=> (((~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(B_229), suc(B_230)))))), rewrite((((~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(B_229), suc(B_230)))) <=> ((~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) <=> ((~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) <=> (((~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))))), rewrite((((~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(B_232), suc(B_233)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(B_232), suc(B_233)))) <=> ((~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) <=> ((~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) <=> (((~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))))), rewrite((((~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) | (~iLEQ(suc(B_231), suc(B_232)))) <=> (((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(B_231), suc(B_232)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(B_231), suc(B_232)))) <=> ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) | (~iLEQ(suc(B_231), suc(B_232)))) <=> ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))))),
% 3.58/2.52 inference(bind,[status(th)],[])).
% 3.58/2.52 tff(267,plain,
% 3.58/2.52 (![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) | (~iLEQ(suc(B_231), suc(B_232)))) <=> ![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 3.58/2.52 inference(quant_intro,[status(thm)],[266])).
% 3.58/2.52 tff(268,axiom,(![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) | (~iLEQ(suc(B_231), suc(B_232))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_193')).
% 3.58/2.52 tff(269,plain,
% 3.58/2.52 (![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 3.58/2.52 inference(modus_ponens,[status(thm)],[268, 267])).
% 3.58/2.52 tff(270,plain,
% 3.58/2.52 (![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 3.58/2.52 inference(modus_ponens,[status(thm)],[269, 265])).
% 3.58/2.52 tff(271,plain,(
% 3.58/2.52 ![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 3.58/2.52 inference(skolemize,[status(sab)],[270])).
% 3.58/2.52 tff(272,plain,
% 3.58/2.52 (![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 3.58/2.52 inference(modus_ponens,[status(thm)],[271, 264])).
% 3.58/2.52 tff(273,plain,
% 3.58/2.52 (((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~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_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.58/2.52 inference(rewrite,[status(thm)],[])).
% 3.58/2.52 tff(274,plain,
% 3.58/2.52 (((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(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)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.58/2.52 inference(rewrite,[status(thm)],[])).
% 3.58/2.52 tff(275,plain,
% 3.58/2.52 (((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(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)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 3.58/2.52 inference(monotonicity,[status(thm)],[274])).
% 3.58/2.52 tff(276,plain,
% 3.58/2.52 (((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(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)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 3.58/2.52 inference(transitivity,[status(thm)],[275, 273])).
% 3.58/2.52 tff(277,plain,
% 3.58/2.52 ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(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)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 3.58/2.52 inference(quant_inst,[status(thm)],[])).
% 3.58/2.52 tff(278,plain,
% 3.58/2.52 ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 3.58/2.52 inference(modus_ponens,[status(thm)],[277, 276])).
% 3.58/2.52 tff(279,plain,
% 3.58/2.52 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 3.58/2.52 inference(unit_resolution,[status(thm)],[278, 272])).
% 3.58/2.52 tff(280,plain,
% 3.58/2.52 (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 3.58/2.52 inference(unit_resolution,[status(thm)],[279, 166, 262])).
% 3.58/2.52 tff(281,plain,
% 3.58/2.52 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 3.58/2.52 inference(unit_resolution,[status(thm)],[253, 239])).
% 3.58/2.52 tff(282,plain,
% 3.58/2.52 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 3.58/2.52 inference(unit_resolution,[status(thm)],[281, 280])).
% 3.58/2.52 tff(283,plain,
% 3.58/2.52 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 3.58/2.52 inference(unit_resolution,[status(thm)],[148, 282])).
% 3.58/2.52 tff(284,plain,
% 3.58/2.52 ($false),
% 3.58/2.52 inference(unit_resolution,[status(thm)],[163, 283, 207, 1])).
% 3.58/2.52 tff(285,plain,(iLEQ(suc(z), suc(z))), inference(lemma,lemma(discharge,[]))).
% 3.58/2.52 tff(286,plain,
% 3.58/2.52 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 3.58/2.52 inference(unit_resolution,[status(thm)],[97, 82])).
% 3.58/2.52 tff(287,plain,
% 3.58/2.52 (tptp_fun__LE_(f(z), s(|'0'|))),
% 3.58/2.52 inference(unit_resolution,[status(thm)],[286, 83])).
% 3.58/2.52 tff(288,plain,
% 3.58/2.52 (tptp_fun__E_(|'0'|, f(z))),
% 3.58/2.52 inference(unit_resolution,[status(thm)],[118, 287])).
% 3.58/2.52 tff(289,plain,
% 3.58/2.52 (^[B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : refl(((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))),
% 3.58/2.52 inference(bind,[status(th)],[])).
% 3.58/2.52 tff(290,plain,
% 3.58/2.52 (![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) <=> ![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 3.58/2.52 inference(quant_intro,[status(thm)],[289])).
% 3.58/2.52 tff(291,plain,
% 3.58/2.52 (![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) <=> ![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 3.58/2.52 inference(rewrite,[status(thm)],[])).
% 3.58/2.52 tff(292,plain,
% 3.58/2.52 (^[B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_255), suc(B_256)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_255), suc(B_256)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_258)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_256), suc(B_257)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_256), suc(B_257)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(A_3)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_255)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_254), suc(B_255)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_254), suc(B_255)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_257), suc(B_258)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_257), suc(B_258)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) | (~tptp_fun__E_(|'0'|, f(B_256)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_256)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_256)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) | (~tptp_fun__E_(|'0'|, f(B_256)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) | (~tptp_fun__E_(|'0'|, f(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_257)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_257)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_257)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) | (~tptp_fun__E_(|'0'|, f(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_257)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))))),
% 3.58/2.53 inference(bind,[status(th)],[])).
% 3.58/2.53 tff(293,plain,
% 3.58/2.53 (![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : (((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) | (~tptp_fun__E_(|'0'|, f(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_257)))) <=> ![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 3.58/2.53 inference(quant_intro,[status(thm)],[292])).
% 3.58/2.53 tff(294,axiom,(![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : (((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) | (~tptp_fun__E_(|'0'|, f(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_257))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_453')).
% 3.58/2.53 tff(295,plain,
% 3.58/2.53 (![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 3.58/2.53 inference(modus_ponens,[status(thm)],[294, 293])).
% 3.58/2.53 tff(296,plain,
% 3.58/2.53 (![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 3.58/2.53 inference(modus_ponens,[status(thm)],[295, 291])).
% 3.58/2.53 tff(297,plain,(
% 3.58/2.53 ![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 3.58/2.53 inference(skolemize,[status(sab)],[296])).
% 3.58/2.53 tff(298,plain,
% 3.58/2.53 (![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 3.58/2.53 inference(modus_ponens,[status(thm)],[297, 290])).
% 3.58/2.53 tff(299,plain,
% 3.58/2.53 (((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.58/2.53 inference(rewrite,[status(thm)],[])).
% 3.58/2.53 tff(300,plain,
% 3.58/2.53 (((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(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)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.58/2.53 inference(rewrite,[status(thm)],[])).
% 3.58/2.53 tff(301,plain,
% 3.58/2.53 (((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(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))))) <=> ((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 3.58/2.53 inference(monotonicity,[status(thm)],[300])).
% 3.58/2.53 tff(302,plain,
% 3.58/2.53 (((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(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))))) <=> ((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.58/2.54 inference(transitivity,[status(thm)],[301, 299])).
% 3.58/2.54 tff(303,plain,
% 3.58/2.54 ((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(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))))),
% 3.58/2.54 inference(quant_inst,[status(thm)],[])).
% 3.58/2.54 tff(304,plain,
% 3.58/2.54 ((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 3.58/2.54 inference(modus_ponens,[status(thm)],[303, 302])).
% 3.58/2.54 tff(305,plain,
% 3.58/2.54 ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[304, 298, 285])).
% 3.58/2.54 tff(306,plain,
% 3.58/2.54 ($false),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[305, 149, 288])).
% 3.58/2.54 tff(307,plain,(tptp_fun__E_(s(|'0'|), f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 3.58/2.54 tff(308,plain,
% 3.58/2.54 (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[193, 31])).
% 3.58/2.54 tff(309,plain,
% 3.58/2.54 (tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[308, 182])).
% 3.58/2.54 tff(310,plain,
% 3.58/2.54 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.58/2.54 inference(rewrite,[status(thm)],[])).
% 3.58/2.54 tff(311,plain,
% 3.58/2.54 (((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(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)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(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(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)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.58/2.54 inference(rewrite,[status(thm)],[])).
% 3.58/2.54 tff(312,plain,
% 3.58/2.54 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(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)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(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(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 3.58/2.54 inference(monotonicity,[status(thm)],[311])).
% 3.58/2.54 tff(313,plain,
% 3.58/2.54 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(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)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(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(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 3.58/2.54 inference(transitivity,[status(thm)],[312, 310])).
% 3.58/2.54 tff(314,plain,
% 3.58/2.54 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(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)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(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(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 3.58/2.54 inference(quant_inst,[status(thm)],[])).
% 3.58/2.54 tff(315,plain,
% 3.58/2.54 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 3.58/2.54 inference(modus_ponens,[status(thm)],[314, 313])).
% 3.58/2.54 tff(316,plain,
% 3.58/2.54 ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[315, 73, 285])).
% 3.58/2.54 tff(317,plain,
% 3.58/2.54 ($false),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[316, 309, 189])).
% 3.58/2.54 tff(318,plain,(tptp_fun__LE_(f(z), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 3.58/2.54 tff(319,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 3.58/2.54 tff(320,plain,
% 3.58/2.54 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[248, 319, 307])).
% 3.58/2.54 tff(321,plain,
% 3.58/2.54 ($false),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[279, 320, 319, 307])).
% 3.58/2.54 tff(322,plain,(~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 3.58/2.54 tff(323,plain,
% 3.58/2.54 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[281, 322])).
% 3.58/2.54 tff(324,plain,
% 3.58/2.54 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[148, 323])).
% 3.58/2.54 tff(325,plain,
% 3.58/2.54 (~tptp_fun__E_(|'0'|, f(z))),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[305, 324])).
% 3.58/2.54 tff(326,plain,
% 3.58/2.54 (~tptp_fun__LE_(f(z), s(|'0'|))),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[118, 325])).
% 3.58/2.54 tff(327,plain,
% 3.58/2.54 (tptp_fun__E_(s(|'0'|), f(z))),
% 3.58/2.54 inference(unit_resolution,[status(thm)],[205, 326, 318])).
% 3.58/2.54 tff(328,plain,
% 3.58/2.54 (((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 3.58/2.54 inference(rewrite,[status(thm)],[])).
% 3.58/2.54 tff(329,plain,
% 3.58/2.54 (((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~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))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 3.58/2.54 inference(rewrite,[status(thm)],[])).
% 3.58/2.54 tff(330,plain,
% 3.58/2.54 (((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~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))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z)))))),
% 3.58/2.54 inference(monotonicity,[status(thm)],[329])).
% 3.58/2.54 tff(331,plain,
% 3.58/2.54 (((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~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))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 3.58/2.55 inference(transitivity,[status(thm)],[330, 328])).
% 3.58/2.55 tff(332,plain,
% 3.58/2.55 ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~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))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 3.58/2.55 inference(quant_inst,[status(thm)],[])).
% 3.58/2.55 tff(333,plain,
% 3.58/2.55 ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 3.58/2.55 inference(modus_ponens,[status(thm)],[332, 331])).
% 3.58/2.55 tff(334,plain,
% 3.58/2.55 ($false),
% 3.58/2.55 inference(unit_resolution,[status(thm)],[333, 272, 327, 307, 285])).
% 3.58/2.55 % SZS output end Proof
%------------------------------------------------------------------------------