TSTP Solution File: SYO664-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYO664-1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 01:41:14 EDT 2022
% Result : Unsatisfiable 1.65s 1.32s
% Output : Proof 1.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO664-1 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Sep 5 15:46:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.65/1.32 % SZS status Unsatisfiable
% 1.65/1.32 % SZS output start Proof
% 1.65/1.32 tff(tptp_fun__E__type, type, (
% 1.65/1.32 tptp_fun__E_: ( $i * $i ) > $o)).
% 1.65/1.32 tff(f_type, type, (
% 1.65/1.32 f: $i > $i)).
% 1.65/1.32 tff(suc_type, type, (
% 1.65/1.32 suc: $i > $i)).
% 1.65/1.32 tff(z_type, type, (
% 1.65/1.32 z: $i)).
% 1.65/1.32 tff(s_type, type, (
% 1.65/1.32 s: $i > $i)).
% 1.65/1.32 tff(tptp_fun__0__type, type, (
% 1.65/1.32 tptp_fun__0_: $i)).
% 1.65/1.32 tff(tptp_fun__LE__type, type, (
% 1.65/1.32 tptp_fun__LE_: ( $i * $i ) > $o)).
% 1.65/1.32 tff(iLEQ_type, type, (
% 1.65/1.32 iLEQ: ( $i * $i ) > $o)).
% 1.65/1.32 tff(1,assumption,(~tptp_fun__LE_(f(z), s(|'0'|))), introduced(assumption)).
% 1.65/1.32 tff(2,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 1.65/1.32 tff(3,plain,
% 1.65/1.32 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(s(|'0'|))) <=> tptp_fun__LE_(f(A), s(s(|'0'|))))),
% 1.65/1.32 inference(bind,[status(th)],[])).
% 1.65/1.32 tff(4,plain,
% 1.65/1.32 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 1.65/1.32 inference(quant_intro,[status(thm)],[3])).
% 1.65/1.32 tff(5,plain,
% 1.65/1.32 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(6,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_58')).
% 1.65/1.32 tff(7,plain,
% 1.65/1.32 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.65/1.32 tff(8,plain,(
% 1.65/1.32 ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 1.65/1.32 inference(skolemize,[status(sab)],[7])).
% 1.65/1.32 tff(9,plain,
% 1.65/1.32 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[8, 4])).
% 1.65/1.32 tff(10,plain,
% 1.65/1.32 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 1.65/1.32 inference(quant_inst,[status(thm)],[])).
% 1.65/1.32 tff(11,plain,
% 1.65/1.32 ($false),
% 1.65/1.32 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 1.65/1.32 tff(12,plain,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.32 tff(13,plain,
% 1.65/1.32 (^[B_42: $i] : refl((tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|))))))),
% 1.65/1.32 inference(bind,[status(th)],[])).
% 1.65/1.32 tff(14,plain,
% 1.65/1.32 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|))))) <=> ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 1.65/1.32 inference(quant_intro,[status(thm)],[13])).
% 1.65/1.32 tff(15,plain,
% 1.65/1.32 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|))))) <=> ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 1.65/1.32 inference(rewrite,[status(thm)],[])).
% 1.65/1.32 tff(16,plain,
% 1.65/1.32 (^[B_42: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_42)))) | tptp_fun__LE_(f(B_42), s(|'0'|))) <=> (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|))))))),
% 1.65/1.32 inference(bind,[status(th)],[])).
% 1.65/1.32 tff(17,plain,
% 1.65/1.32 (![B_42: $i] : (((~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_42)))) | tptp_fun__LE_(f(B_42), s(|'0'|))) <=> ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 1.65/1.32 inference(quant_intro,[status(thm)],[16])).
% 1.65/1.32 tff(18,axiom,(![B_42: $i] : (((~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_42)))) | tptp_fun__LE_(f(B_42), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_83')).
% 1.65/1.32 tff(19,plain,
% 1.65/1.32 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 1.65/1.32 inference(modus_ponens,[status(thm)],[18, 17])).
% 1.65/1.32 tff(20,plain,
% 1.65/1.32 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.65/1.33 tff(21,plain,(
% 1.65/1.33 ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 1.65/1.33 inference(skolemize,[status(sab)],[20])).
% 1.65/1.33 tff(22,plain,
% 1.65/1.33 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.65/1.33 tff(23,plain,
% 1.65/1.33 (((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(24,plain,
% 1.65/1.33 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(25,plain,
% 1.65/1.33 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.65/1.33 tff(26,plain,
% 1.65/1.33 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[25, 22])).
% 1.65/1.33 tff(27,plain,
% 1.65/1.33 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[26, 12])).
% 1.65/1.33 tff(28,plain,
% 1.65/1.33 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[27, 1])).
% 1.65/1.33 tff(29,plain,
% 1.65/1.33 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(30,plain,
% 1.65/1.33 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[29, 9])).
% 1.65/1.33 tff(31,plain,
% 1.65/1.33 (^[B_42: $i] : refl((tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))) <=> (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))))),
% 1.65/1.33 inference(bind,[status(th)],[])).
% 1.65/1.33 tff(32,plain,
% 1.65/1.33 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))) <=> ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 1.65/1.33 inference(quant_intro,[status(thm)],[31])).
% 1.65/1.33 tff(33,plain,
% 1.65/1.33 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))) <=> ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(34,plain,
% 1.65/1.33 (^[B_42: $i] : rewrite((((~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))) | tptp_fun__LE_(f(B_42), s(|'0'|))) <=> (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))))),
% 1.65/1.33 inference(bind,[status(th)],[])).
% 1.65/1.33 tff(35,plain,
% 1.65/1.33 (![B_42: $i] : (((~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))) | tptp_fun__LE_(f(B_42), s(|'0'|))) <=> ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 1.65/1.33 inference(quant_intro,[status(thm)],[34])).
% 1.65/1.33 tff(36,axiom,(![B_42: $i] : (((~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))) | tptp_fun__LE_(f(B_42), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_20')).
% 1.65/1.33 tff(37,plain,
% 1.65/1.33 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.65/1.33 tff(38,plain,
% 1.65/1.33 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[37, 33])).
% 1.65/1.33 tff(39,plain,(
% 1.65/1.33 ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 1.65/1.33 inference(skolemize,[status(sab)],[38])).
% 1.65/1.33 tff(40,plain,
% 1.65/1.33 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[39, 32])).
% 1.65/1.33 tff(41,plain,
% 1.65/1.33 (((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))) <=> ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(42,plain,
% 1.65/1.33 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(43,plain,
% 1.65/1.33 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.65/1.33 tff(44,plain,
% 1.65/1.33 (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[43, 40])).
% 1.65/1.33 tff(45,plain,
% 1.65/1.33 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z))),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[44, 30])).
% 1.65/1.33 tff(46,plain,
% 1.65/1.33 (tptp_fun__E_(s(|'0'|), f(z))),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[45, 1])).
% 1.65/1.33 tff(47,plain,
% 1.65/1.33 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))),
% 1.65/1.33 inference(bind,[status(th)],[])).
% 1.65/1.33 tff(48,plain,
% 1.65/1.33 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 1.65/1.33 inference(quant_intro,[status(thm)],[47])).
% 1.65/1.33 tff(49,plain,
% 1.65/1.33 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(50,plain,
% 1.65/1.33 (^[A_1: $i] : rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))),
% 1.65/1.33 inference(bind,[status(th)],[])).
% 1.65/1.33 tff(51,plain,
% 1.65/1.33 (![A_1: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(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(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 1.65/1.33 inference(quant_intro,[status(thm)],[50])).
% 1.65/1.33 tff(52,axiom,(![A_1: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_50')).
% 1.65/1.33 tff(53,plain,
% 1.65/1.33 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[52, 51])).
% 1.65/1.33 tff(54,plain,
% 1.65/1.33 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[53, 49])).
% 1.65/1.33 tff(55,plain,(
% 1.65/1.33 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 1.65/1.33 inference(skolemize,[status(sab)],[54])).
% 1.65/1.33 tff(56,plain,
% 1.65/1.33 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[55, 48])).
% 1.65/1.33 tff(57,plain,
% 1.65/1.33 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(58,plain,
% 1.65/1.33 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 1.65/1.33 inference(quant_inst,[status(thm)],[])).
% 1.65/1.33 tff(59,plain,
% 1.65/1.33 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 1.65/1.33 inference(modus_ponens,[status(thm)],[58, 57])).
% 1.65/1.33 tff(60,plain,
% 1.65/1.33 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[59, 56])).
% 1.65/1.33 tff(61,plain,
% 1.65/1.33 (iLEQ(suc(z), suc(z))),
% 1.65/1.33 inference(unit_resolution,[status(thm)],[60, 46, 28])).
% 1.65/1.33 tff(62,plain,
% 1.65/1.33 (^[B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : refl(((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))),
% 1.65/1.33 inference(bind,[status(th)],[])).
% 1.65/1.33 tff(63,plain,
% 1.65/1.33 (![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) <=> ![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 1.65/1.33 inference(quant_intro,[status(thm)],[62])).
% 1.65/1.33 tff(64,plain,
% 1.65/1.33 (![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) <=> ![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 1.65/1.33 inference(rewrite,[status(thm)],[])).
% 1.65/1.33 tff(65,plain,
% 1.65/1.33 (^[B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(A_1), suc(B_43)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(A_1), suc(B_43)))) <=> ((~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) <=> ((~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) <=> (((~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))))), rewrite((((~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(B_44), suc(B_45)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(B_44), suc(B_45)))) <=> ((~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) <=> ((~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) <=> (((~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))))), rewrite((((~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(B_45), suc(B_46)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(B_45), suc(B_46)))) <=> ((~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) <=> ((~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) | (~iLEQ(suc(B_43), suc(B_44)))) <=> (((~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(B_43), suc(B_44)))))), rewrite((((~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(B_43), suc(B_44)))) <=> ((~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) | (~iLEQ(suc(B_43), suc(B_44)))) <=> ((~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) | (~iLEQ(suc(B_43), suc(B_44)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_44))))) <=> (((~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_44))))))), rewrite((((~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_44))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) | (~iLEQ(suc(B_43), suc(B_44)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_44))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))))),
% 1.65/1.34 inference(bind,[status(th)],[])).
% 1.65/1.34 tff(66,plain,
% 1.65/1.34 (![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) | (~iLEQ(suc(B_43), suc(B_44)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_44))))) <=> ![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 1.65/1.34 inference(quant_intro,[status(thm)],[65])).
% 1.65/1.34 tff(67,axiom,(![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) | (~iLEQ(suc(B_43), suc(B_44)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_44)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_37')).
% 1.65/1.34 tff(68,plain,
% 1.65/1.34 (![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[67, 66])).
% 1.65/1.34 tff(69,plain,
% 1.65/1.34 (![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[68, 64])).
% 1.65/1.34 tff(70,plain,(
% 1.65/1.34 ![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 1.65/1.34 inference(skolemize,[status(sab)],[69])).
% 1.65/1.34 tff(71,plain,
% 1.65/1.34 (![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[70, 63])).
% 1.65/1.34 tff(72,plain,
% 1.65/1.34 (((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(73,plain,
% 1.65/1.34 (((~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))) | (~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)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(74,plain,
% 1.65/1.34 (((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~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))) | (~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)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 1.65/1.34 inference(monotonicity,[status(thm)],[73])).
% 1.65/1.34 tff(75,plain,
% 1.65/1.34 (((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~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))) | (~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)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 1.65/1.34 inference(transitivity,[status(thm)],[74, 72])).
% 1.65/1.34 tff(76,plain,
% 1.65/1.34 ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~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))) | (~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)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 1.65/1.34 inference(quant_inst,[status(thm)],[])).
% 1.65/1.34 tff(77,plain,
% 1.65/1.34 ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.65/1.34 tff(78,plain,
% 1.65/1.34 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[77, 71])).
% 1.65/1.34 tff(79,plain,
% 1.65/1.34 ($false),
% 1.65/1.34 inference(unit_resolution,[status(thm)],[78, 28, 46, 61])).
% 1.65/1.34 tff(80,plain,(tptp_fun__LE_(f(z), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 1.65/1.34 tff(81,plain,
% 1.65/1.34 (^[B_60: $i] : refl(((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60))) <=> ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60))))),
% 1.65/1.34 inference(bind,[status(th)],[])).
% 1.65/1.34 tff(82,plain,
% 1.65/1.34 (![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60))) <=> ![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 1.65/1.34 inference(quant_intro,[status(thm)],[81])).
% 1.65/1.34 tff(83,plain,
% 1.65/1.34 (![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60))) <=> ![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 1.65/1.34 inference(rewrite,[status(thm)],[])).
% 1.65/1.34 tff(84,plain,
% 1.65/1.34 (^[B_60: $i] : rewrite((((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_60))) | tptp_fun__LE_(f(B_60), |'0'|)) <=> ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60))))),
% 1.65/1.34 inference(bind,[status(th)],[])).
% 1.65/1.34 tff(85,plain,
% 1.65/1.34 (![B_60: $i] : (((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_60))) | tptp_fun__LE_(f(B_60), |'0'|)) <=> ![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 1.65/1.34 inference(quant_intro,[status(thm)],[84])).
% 1.65/1.34 tff(86,axiom,(![B_60: $i] : (((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_60))) | tptp_fun__LE_(f(B_60), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_94')).
% 1.65/1.34 tff(87,plain,
% 1.65/1.34 (![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.65/1.34 tff(88,plain,
% 1.65/1.34 (![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[87, 83])).
% 1.65/1.34 tff(89,plain,(
% 1.65/1.34 ![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 1.65/1.34 inference(skolemize,[status(sab)],[88])).
% 1.65/1.34 tff(90,plain,
% 1.65/1.34 (![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 1.65/1.34 inference(modus_ponens,[status(thm)],[89, 82])).
% 1.65/1.34 tff(91,plain,
% 1.75/1.34 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 1.75/1.34 inference(rewrite,[status(thm)],[])).
% 1.75/1.34 tff(92,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_70')).
% 1.75/1.34 tff(93,plain,
% 1.75/1.34 (~tptp_fun__LE_(f(z), |'0'|)),
% 1.75/1.34 inference(modus_ponens,[status(thm)],[92, 91])).
% 1.75/1.34 tff(94,plain,
% 1.75/1.34 (((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 1.75/1.34 inference(rewrite,[status(thm)],[])).
% 1.75/1.34 tff(95,plain,
% 1.75/1.34 (((~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)))),
% 1.75/1.34 inference(rewrite,[status(thm)],[])).
% 1.75/1.34 tff(96,plain,
% 1.75/1.34 (((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))))),
% 1.75/1.34 inference(monotonicity,[status(thm)],[95])).
% 1.75/1.34 tff(97,plain,
% 1.75/1.34 (((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 1.75/1.34 inference(transitivity,[status(thm)],[96, 94])).
% 1.75/1.34 tff(98,plain,
% 1.75/1.34 ((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))),
% 1.75/1.34 inference(quant_inst,[status(thm)],[])).
% 1.75/1.34 tff(99,plain,
% 1.75/1.34 ((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 1.75/1.34 inference(modus_ponens,[status(thm)],[98, 97])).
% 1.75/1.34 tff(100,plain,
% 1.75/1.34 ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 1.75/1.34 inference(unit_resolution,[status(thm)],[99, 93, 90])).
% 1.75/1.34 tff(101,plain,
% 1.75/1.34 (tptp_fun__E_(|'0'|, f(z))),
% 1.75/1.34 inference(unit_resolution,[status(thm)],[100, 80])).
% 1.75/1.34 tff(102,assumption,(tptp_fun__E_(|'0'|, f(suc(z)))), introduced(assumption)).
% 1.75/1.34 tff(103,assumption,(tptp_fun__E_(|'0'|, f(z))), introduced(assumption)).
% 1.75/1.34 tff(104,plain,
% 1.75/1.34 (^[A_2: $i] : refl((iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))),
% 1.75/1.34 inference(bind,[status(th)],[])).
% 1.75/1.34 tff(105,plain,
% 1.75/1.34 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 1.75/1.34 inference(quant_intro,[status(thm)],[104])).
% 1.75/1.34 tff(106,plain,
% 1.75/1.34 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 1.75/1.34 inference(rewrite,[status(thm)],[])).
% 1.75/1.34 tff(107,plain,
% 1.75/1.34 (^[A_2: $i] : rewrite((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))),
% 1.75/1.34 inference(bind,[status(th)],[])).
% 1.75/1.34 tff(108,plain,
% 1.75/1.34 (![A_2: $i] : (((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'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_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 1.75/1.34 inference(quant_intro,[status(thm)],[107])).
% 1.75/1.34 tff(109,axiom,(![A_2: $i] : (((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6')).
% 1.75/1.34 tff(110,plain,
% 1.75/1.34 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 1.75/1.34 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.75/1.34 tff(111,plain,
% 1.75/1.34 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 1.75/1.34 inference(modus_ponens,[status(thm)],[110, 106])).
% 1.75/1.34 tff(112,plain,(
% 1.75/1.34 ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 1.75/1.34 inference(skolemize,[status(sab)],[111])).
% 1.75/1.34 tff(113,plain,
% 1.75/1.34 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 1.75/1.34 inference(modus_ponens,[status(thm)],[112, 105])).
% 1.75/1.34 tff(114,plain,
% 1.75/1.34 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 1.75/1.34 inference(rewrite,[status(thm)],[])).
% 1.75/1.34 tff(115,plain,
% 1.75/1.34 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 1.75/1.34 inference(quant_inst,[status(thm)],[])).
% 1.75/1.34 tff(116,plain,
% 1.75/1.34 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 1.75/1.34 inference(modus_ponens,[status(thm)],[115, 114])).
% 1.75/1.34 tff(117,plain,
% 1.75/1.34 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 1.75/1.34 inference(unit_resolution,[status(thm)],[116, 113])).
% 1.75/1.34 tff(118,plain,
% 1.75/1.34 (iLEQ(suc(z), suc(z))),
% 1.75/1.34 inference(unit_resolution,[status(thm)],[117, 103, 102])).
% 1.75/1.34 tff(119,plain,
% 1.75/1.34 (^[B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : refl(((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) <=> ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))),
% 1.75/1.34 inference(bind,[status(th)],[])).
% 1.75/1.34 tff(120,plain,
% 1.75/1.34 (![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) <=> ![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 1.75/1.34 inference(quant_intro,[status(thm)],[119])).
% 1.75/1.34 tff(121,plain,
% 1.75/1.34 (![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) <=> ![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 1.75/1.34 inference(rewrite,[status(thm)],[])).
% 1.75/1.34 tff(122,plain,
% 1.75/1.34 (^[B_63: $i, B_64: $i, B_62: $i, B_61: $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(rewrite((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(A_2), suc(B_61)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(A_2), suc(B_61)))) <=> ((~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) <=> ((~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), ((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) <=> (((~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(B_61), suc(B_62)))))), rewrite((((~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(B_61), suc(B_62)))) <=> ((~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), ((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) <=> ((~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), (((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) <=> (((~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))))), rewrite((((~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), ((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(A_2)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), ((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), (((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) <=> (((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(B_62), suc(B_63)))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(B_62), suc(B_63)))) <=> ((~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) <=> ((~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), ((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) <=> (((~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))))), rewrite((((~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) <=> ((~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), ((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) <=> ((~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), (((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) <=> (((~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(B_63), suc(B_64)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(B_63), suc(B_64)))) <=> ((~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) <=> ((~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), ((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) <=> (((~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))))), rewrite((((~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), ((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), (((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_61)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_61)))) <=> ((~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) <=> ((~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) <=> (((~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) | (~tptp_fun__E_(|'0'|, f(B_62)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_62)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_62)))) <=> ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) | (~tptp_fun__E_(|'0'|, f(B_62)))) <=> ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))))),
% 1.75/1.35 inference(bind,[status(th)],[])).
% 1.75/1.35 tff(123,plain,
% 1.75/1.35 (![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) | (~tptp_fun__E_(|'0'|, f(B_62)))) <=> ![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 1.75/1.35 inference(quant_intro,[status(thm)],[122])).
% 1.75/1.35 tff(124,axiom,(![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) | (~tptp_fun__E_(|'0'|, f(B_62))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_66')).
% 1.75/1.35 tff(125,plain,
% 1.75/1.35 (![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 1.75/1.35 inference(modus_ponens,[status(thm)],[124, 123])).
% 1.75/1.35 tff(126,plain,
% 1.75/1.35 (![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 1.75/1.35 inference(modus_ponens,[status(thm)],[125, 121])).
% 1.75/1.35 tff(127,plain,(
% 1.75/1.35 ![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 1.75/1.35 inference(skolemize,[status(sab)],[126])).
% 1.75/1.35 tff(128,plain,
% 1.75/1.35 (![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 1.75/1.35 inference(modus_ponens,[status(thm)],[127, 120])).
% 1.75/1.35 tff(129,plain,
% 1.75/1.35 (((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 1.75/1.35 inference(rewrite,[status(thm)],[])).
% 1.75/1.35 tff(130,plain,
% 1.75/1.35 (((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))) <=> ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 1.75/1.35 inference(rewrite,[status(thm)],[])).
% 1.75/1.35 tff(131,plain,
% 1.75/1.35 (((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))) <=> ((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))))),
% 1.75/1.35 inference(monotonicity,[status(thm)],[130])).
% 1.75/1.35 tff(132,plain,
% 1.75/1.35 (((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))) <=> ((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 1.75/1.35 inference(transitivity,[status(thm)],[131, 129])).
% 1.75/1.35 tff(133,plain,
% 1.75/1.35 ((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 1.75/1.35 inference(quant_inst,[status(thm)],[])).
% 1.75/1.35 tff(134,plain,
% 1.75/1.35 ((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 1.75/1.35 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.75/1.35 tff(135,plain,
% 1.75/1.35 ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 1.75/1.35 inference(unit_resolution,[status(thm)],[134, 128])).
% 1.75/1.35 tff(136,plain,
% 1.75/1.35 ($false),
% 1.75/1.35 inference(unit_resolution,[status(thm)],[135, 118, 103, 102])).
% 1.75/1.35 tff(137,plain,((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.35 tff(138,plain,
% 1.75/1.35 (~tptp_fun__E_(|'0'|, f(suc(z)))),
% 1.75/1.35 inference(unit_resolution,[status(thm)],[137, 101])).
% 1.75/1.35 tff(139,plain,
% 1.75/1.35 (^[B_60: $i] : refl((tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) <=> (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))))),
% 1.75/1.35 inference(bind,[status(th)],[])).
% 1.75/1.35 tff(140,plain,
% 1.75/1.35 (![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) <=> ![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 1.75/1.35 inference(quant_intro,[status(thm)],[139])).
% 1.75/1.35 tff(141,plain,
% 1.75/1.35 (![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) <=> ![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 1.75/1.35 inference(rewrite,[status(thm)],[])).
% 1.75/1.35 tff(142,plain,
% 1.75/1.36 (^[B_60: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) | tptp_fun__LE_(f(B_60), |'0'|)) <=> (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))))),
% 1.75/1.36 inference(bind,[status(th)],[])).
% 1.75/1.36 tff(143,plain,
% 1.75/1.36 (![B_60: $i] : (((~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) | tptp_fun__LE_(f(B_60), |'0'|)) <=> ![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 1.75/1.36 inference(quant_intro,[status(thm)],[142])).
% 1.75/1.36 tff(144,axiom,(![B_60: $i] : (((~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) | tptp_fun__LE_(f(B_60), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_117')).
% 1.75/1.36 tff(145,plain,
% 1.75/1.36 (![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 1.75/1.36 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.75/1.36 tff(146,plain,
% 1.75/1.36 (![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 1.75/1.36 inference(modus_ponens,[status(thm)],[145, 141])).
% 1.75/1.36 tff(147,plain,(
% 1.75/1.36 ![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 1.75/1.36 inference(skolemize,[status(sab)],[146])).
% 1.75/1.36 tff(148,plain,
% 1.75/1.36 (![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 1.75/1.36 inference(modus_ponens,[status(thm)],[147, 140])).
% 1.75/1.36 tff(149,plain,
% 1.75/1.36 (((~![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 1.75/1.36 inference(rewrite,[status(thm)],[])).
% 1.75/1.36 tff(150,plain,
% 1.75/1.36 ((~![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 1.75/1.36 inference(quant_inst,[status(thm)],[])).
% 1.75/1.36 tff(151,plain,
% 1.75/1.36 ((~![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 1.75/1.36 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.75/1.36 tff(152,plain,
% 1.75/1.36 ((~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 1.75/1.36 inference(unit_resolution,[status(thm)],[151, 93, 148])).
% 1.75/1.36 tff(153,plain,
% 1.75/1.36 (~tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 1.75/1.36 inference(unit_resolution,[status(thm)],[152, 138])).
% 1.75/1.36 tff(154,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), introduced(assumption)).
% 1.75/1.36 tff(155,plain,
% 1.75/1.36 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))),
% 1.75/1.36 inference(quant_inst,[status(thm)],[])).
% 1.75/1.36 tff(156,plain,
% 1.75/1.36 ($false),
% 1.75/1.36 inference(unit_resolution,[status(thm)],[155, 9, 154])).
% 1.75/1.36 tff(157,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.36 tff(158,plain,
% 1.75/1.36 (((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))) <=> ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 1.75/1.36 inference(rewrite,[status(thm)],[])).
% 1.75/1.36 tff(159,plain,
% 1.75/1.36 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 1.75/1.36 inference(quant_inst,[status(thm)],[])).
% 1.75/1.36 tff(160,plain,
% 1.75/1.36 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 1.75/1.36 inference(modus_ponens,[status(thm)],[159, 158])).
% 1.75/1.36 tff(161,plain,
% 1.75/1.36 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 1.75/1.36 inference(unit_resolution,[status(thm)],[160, 22, 157])).
% 1.75/1.36 tff(162,plain,
% 1.75/1.36 (tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 1.75/1.36 inference(unit_resolution,[status(thm)],[161, 153])).
% 1.75/1.36 tff(163,plain,
% 1.75/1.36 (((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 1.75/1.36 inference(rewrite,[status(thm)],[])).
% 1.75/1.36 tff(164,plain,
% 1.75/1.36 ((tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))) <=> (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 1.75/1.36 inference(rewrite,[status(thm)],[])).
% 1.75/1.36 tff(165,plain,
% 1.75/1.36 (((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (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_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))))),
% 1.75/1.36 inference(monotonicity,[status(thm)],[164])).
% 1.75/1.36 tff(166,plain,
% 1.75/1.36 (((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (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_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 1.75/1.36 inference(transitivity,[status(thm)],[165, 163])).
% 1.75/1.36 tff(167,plain,
% 1.75/1.36 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (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))))),
% 1.75/1.36 inference(quant_inst,[status(thm)],[])).
% 1.75/1.36 tff(168,plain,
% 1.75/1.36 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 1.75/1.36 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.75/1.36 tff(169,plain,
% 1.75/1.36 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 1.75/1.36 inference(unit_resolution,[status(thm)],[168, 40, 12])).
% 1.75/1.36 tff(170,plain,
% 1.75/1.36 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 1.75/1.36 inference(unit_resolution,[status(thm)],[169, 153])).
% 1.75/1.36 tff(171,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 1.75/1.36 tff(172,assumption,(tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 1.75/1.36 tff(173,plain,
% 1.75/1.36 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 1.75/1.36 inference(rewrite,[status(thm)],[])).
% 1.75/1.36 tff(174,plain,
% 1.75/1.36 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 1.75/1.36 inference(rewrite,[status(thm)],[])).
% 1.75/1.36 tff(175,plain,
% 1.75/1.36 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))))),
% 1.75/1.36 inference(monotonicity,[status(thm)],[174])).
% 1.75/1.36 tff(176,plain,
% 1.75/1.36 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 1.75/1.36 inference(transitivity,[status(thm)],[175, 173])).
% 1.75/1.36 tff(177,plain,
% 1.75/1.36 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 1.75/1.36 inference(quant_inst,[status(thm)],[])).
% 1.75/1.36 tff(178,plain,
% 1.75/1.36 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 1.75/1.36 inference(modus_ponens,[status(thm)],[177, 176])).
% 1.75/1.36 tff(179,plain,
% 1.75/1.36 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 1.75/1.36 inference(unit_resolution,[status(thm)],[178, 56])).
% 1.75/1.36 tff(180,plain,
% 1.75/1.36 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 1.75/1.36 inference(unit_resolution,[status(thm)],[179, 172, 171])).
% 1.75/1.36 tff(181,plain,
% 1.75/1.36 (((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~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_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 1.75/1.36 inference(rewrite,[status(thm)],[])).
% 1.75/1.36 tff(182,plain,
% 1.75/1.36 (((~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)))) | (~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))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 1.75/1.36 inference(rewrite,[status(thm)],[])).
% 1.75/1.36 tff(183,plain,
% 1.75/1.36 (((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~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)))) | (~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))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 1.75/1.36 inference(monotonicity,[status(thm)],[182])).
% 1.75/1.36 tff(184,plain,
% 1.75/1.36 (((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~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)))) | (~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))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 1.75/1.36 inference(transitivity,[status(thm)],[183, 181])).
% 1.75/1.36 tff(185,plain,
% 1.75/1.36 ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~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)))) | (~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))))) | (~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))))))),
% 1.75/1.36 inference(quant_inst,[status(thm)],[])).
% 1.75/1.36 tff(186,plain,
% 1.75/1.36 ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 1.75/1.36 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.75/1.36 tff(187,plain,
% 1.75/1.36 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 1.75/1.36 inference(unit_resolution,[status(thm)],[186, 71])).
% 1.75/1.36 tff(188,plain,
% 1.75/1.36 ($false),
% 1.75/1.36 inference(unit_resolution,[status(thm)],[187, 180, 172, 171])).
% 1.75/1.36 tff(189,plain,((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.36 tff(190,plain,
% 1.75/1.36 ($false),
% 1.75/1.36 inference(unit_resolution,[status(thm)],[189, 170, 162])).
% 1.75/1.36 % SZS output end Proof
%------------------------------------------------------------------------------