%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO666-1 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 : Sat Jun 21 05:42:04 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO666-1 : TPTP v9.0.0. Released v7.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 : Fri Jun 20 13:26:20 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% 0.18/0.37 tff(iLEQ_type, type, (
% 0.18/0.37 iLEQ: ( $i * $i ) > $o)).
% 0.18/0.37 tff(suc_type, type, (
% 0.18/0.37 suc: $i > $i)).
% 0.18/0.37 tff(z_type, type, (
% 0.18/0.37 z: $i)).
% 0.18/0.37 tff(tptp_fun__E__type, type, (
% 0.18/0.37 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.18/0.37 tff(f_type, type, (
% 0.18/0.37 f: $i > $i)).
% 0.18/0.37 tff(tptp_fun__0__type, type, (
% 0.18/0.37 tptp_fun__0_: $i)).
% 0.18/0.37 tff(tptp_fun__LE__type, type, (
% 0.18/0.37 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.18/0.37 tff(s_type, type, (
% 0.18/0.37 s: $i > $i)).
% 0.18/0.37 tff(1,assumption,(~tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 0.18/0.37 tff(2,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 0.18/0.37 tff(3,plain,
% 0.18/0.37 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(s(|'0'|))) <=> tptp_fun__LE_(f(A), s(s(|'0'|))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(4,plain,
% 0.18/0.37 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.37 tff(5,plain,
% 0.18/0.37 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(6,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_83')).
% 0.18/0.37 tff(7,plain,
% 0.18/0.37 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.37 tff(8,plain,(
% 0.18/0.37 ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.18/0.37 inference(skolemize,[status(sab)],[7])).
% 0.18/0.37 tff(9,plain,
% 0.18/0.37 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.37 tff(10,plain,
% 0.18/0.37 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(11,plain,
% 0.18/0.37 ($false),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.18/0.37 tff(12,plain,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.37 tff(13,plain,
% 0.18/0.37 (^[B_68: $i] : refl((tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(14,plain,
% 0.18/0.37 (![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|))))) <=> ![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|)))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.37 tff(15,plain,
% 0.18/0.37 (![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|))))) <=> ![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|)))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (^[B_68: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_68)))) | tptp_fun__LE_(f(B_68), s(|'0'|))) <=> (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (![B_68: $i] : (((~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_68)))) | tptp_fun__LE_(f(B_68), s(|'0'|))) <=> ![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|)))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.37 tff(18,axiom,(![B_68: $i] : (((~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_68)))) | tptp_fun__LE_(f(B_68), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_29')).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|)))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.38 tff(21,plain,(
% 0.18/0.38 ![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|)))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[20])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 (((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), 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_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), 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'|)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 ((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), 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'|)))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 ((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), 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'|))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[25, 22])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[26, 12])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[27, 1])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 (^[B_93: $i] : refl((tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93))) <=> (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93))) <=> ![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[29])).
% 0.18/0.38 tff(31,plain,
% 0.18/0.38 (![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93))) <=> ![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 (^[B_93: $i] : rewrite((((~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93))) | tptp_fun__LE_(f(B_93), |'0'|)) <=> (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 (![B_93: $i] : (((~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93))) | tptp_fun__LE_(f(B_93), |'0'|)) <=> ![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.18/0.38 tff(34,axiom,(![B_93: $i] : (((~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93))) | tptp_fun__LE_(f(B_93), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_42')).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 (![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.18/0.38 tff(37,plain,(
% 0.18/0.38 ![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[36])).
% 0.18/0.38 tff(38,plain,
% 0.18/0.38 (![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.18/0.38 tff(39,plain,
% 0.18/0.38 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(40,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_98')).
% 0.18/0.38 tff(41,plain,
% 0.18/0.38 (~tptp_fun__LE_(f(z), |'0'|)),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.38 tff(42,plain,
% 0.18/0.38 (((~![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(43,plain,
% 0.18/0.38 ((~![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(44,plain,
% 0.18/0.38 ((~![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(B_93), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_93)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.18/0.38 tff(45,plain,
% 0.18/0.38 ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[44, 41, 38])).
% 0.18/0.38 tff(46,plain,
% 0.18/0.38 (tptp_fun__E_(|'0'|, f(z))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[45, 28])).
% 0.18/0.38 tff(47,plain,
% 0.18/0.38 (^[B_68: $i] : refl((tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(48,plain,
% 0.18/0.38 (![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|))))) <=> ![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[47])).
% 0.18/0.38 tff(49,plain,
% 0.18/0.38 (![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|))))) <=> ![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(50,plain,
% 0.18/0.38 (^[B_68: $i] : rewrite((((~tptp_fun__LE_(f(B_68), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_68))) | tptp_fun__LE_(f(B_68), s(|'0'|))) <=> (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(51,plain,
% 0.18/0.38 (![B_68: $i] : (((~tptp_fun__LE_(f(B_68), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_68))) | tptp_fun__LE_(f(B_68), s(|'0'|))) <=> ![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[50])).
% 0.18/0.38 tff(52,axiom,(![B_68: $i] : (((~tptp_fun__LE_(f(B_68), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_68))) | tptp_fun__LE_(f(B_68), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_185')).
% 0.18/0.38 tff(53,plain,
% 0.18/0.38 (![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.18/0.38 tff(54,plain,
% 0.18/0.38 (![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.18/0.38 tff(55,plain,(
% 0.18/0.38 ![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))),
% 0.18/0.38 inference(skolemize,[status(sab)],[54])).
% 0.18/0.38 tff(56,plain,
% 0.18/0.38 (![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.18/0.38 tff(57,plain,
% 0.18/0.38 (((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))) <=> ((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(58,plain,
% 0.18/0.38 ((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'|))))) <=> (tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(59,plain,
% 0.18/0.38 (((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[58])).
% 0.18/0.38 tff(60,plain,
% 0.18/0.38 (((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[59, 57])).
% 0.18/0.38 tff(61,plain,
% 0.18/0.38 ((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(62,plain,
% 0.18/0.38 ((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.18/0.38 tff(63,plain,
% 0.18/0.38 (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[62, 56, 12])).
% 0.18/0.38 tff(64,plain,
% 0.18/0.38 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[63, 1])).
% 0.18/0.38 tff(65,plain,
% 0.18/0.38 (^[B_93: $i] : refl((tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93)))) <=> (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93)))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(66,plain,
% 0.18/0.38 (![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93)))) <=> ![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93)))) <=> ![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 (^[B_93: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93)))) | tptp_fun__LE_(f(B_93), |'0'|)) <=> (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 (![B_93: $i] : (((~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93)))) | tptp_fun__LE_(f(B_93), |'0'|)) <=> ![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.39 tff(70,axiom,(![B_93: $i] : (((~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93)))) | tptp_fun__LE_(f(B_93), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_123')).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 (![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 (![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.18/0.39 tff(73,plain,(
% 0.18/0.39 ![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[72])).
% 0.18/0.39 tff(74,plain,
% 0.18/0.39 (![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 (((~![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 ((~![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 ((~![B_93: $i] : (tptp_fun__LE_(f(B_93), |'0'|) | (~tptp_fun__LE_(f(suc(B_93)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_93))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 ((~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[77, 41, 74])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[78, 64])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(81,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[80])).
% 0.18/0.39 tff(82,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(83,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(84,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.39 tff(85,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_12')).
% 0.18/0.39 tff(86,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.39 tff(87,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.18/0.39 tff(88,plain,(
% 0.18/0.39 ![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)))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[87])).
% 0.18/0.39 tff(89,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.18/0.39 tff(90,plain,
% 0.18/0.39 (((~![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)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(91,plain,
% 0.18/0.39 ((~![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)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(92,plain,
% 0.18/0.39 ((~![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))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.18/0.39 tff(93,plain,
% 0.18/0.39 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[92, 89])).
% 0.18/0.39 tff(94,plain,
% 0.18/0.39 (iLEQ(suc(z), suc(z))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[93, 79, 46])).
% 0.18/0.39 tff(95,plain,
% 0.18/0.39 (^[B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : refl(((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) <=> ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(96,plain,
% 0.18/0.39 (![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) <=> ![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[95])).
% 0.18/0.39 tff(97,plain,
% 0.18/0.39 (![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) <=> ![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(98,plain,
% 0.18/0.39 (^[B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), (((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98)))) <=> ((~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), (((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) <=> ((~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), ((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) <=> (((~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))))), rewrite((((~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), ((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), (((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(A_2)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), (((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), ((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) <=> (((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), ((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), (((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(B_97)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(B_97)))) <=> ((~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), (((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) <=> ((~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), ((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) <=> (((~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) <=> ((~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), ((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) <=> ((~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), (((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) <=> (((~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(B_96)))))), rewrite((((~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) <=> ((~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), (((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) <=> ((~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), ((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) <=> (((~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~iLEQ(suc(B_94), suc(B_95)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~iLEQ(suc(B_94), suc(B_95)))) <=> ((~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), ((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) <=> ((~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), (((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) <=> (((~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))))), rewrite((((~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), (((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), ((((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) | (~tptp_fun__E_(|'0'|, f(B_94)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(B_94)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(B_94)))) <=> ((~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), ((((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) | (~tptp_fun__E_(|'0'|, f(B_94)))) <=> ((~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), (((((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) | (~tptp_fun__E_(|'0'|, f(B_94)))) | (~iLEQ(suc(A_2), suc(B_94)))) <=> (((~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~iLEQ(suc(A_2), suc(B_94)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~iLEQ(suc(A_2), suc(B_94)))) <=> ((~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), (((((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) | (~tptp_fun__E_(|'0'|, f(B_94)))) | (~iLEQ(suc(A_2), suc(B_94)))) <=> ((~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), ((((((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) | (~tptp_fun__E_(|'0'|, f(B_94)))) | (~iLEQ(suc(A_2), suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(suc(B_95))))) <=> (((~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(suc(B_95))))))), rewrite((((~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(suc(B_95))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), ((((((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) | (~tptp_fun__E_(|'0'|, f(B_94)))) | (~iLEQ(suc(A_2), suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(suc(B_95))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), (((((((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) | (~tptp_fun__E_(|'0'|, f(B_94)))) | (~iLEQ(suc(A_2), suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(suc(B_95))))) | (~tptp_fun__E_(|'0'|, f(B_98)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(B_98)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(B_98)))) <=> ((~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), (((((((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) | (~tptp_fun__E_(|'0'|, f(B_94)))) | (~iLEQ(suc(A_2), suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(suc(B_95))))) | (~tptp_fun__E_(|'0'|, f(B_98)))) <=> ((~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))))), ((((((((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) | (~tptp_fun__E_(|'0'|, f(B_94)))) | (~iLEQ(suc(A_2), suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(suc(B_95))))) | (~tptp_fun__E_(|'0'|, f(B_98)))) | (~tptp_fun__E_(|'0'|, f(B_95)))) <=> (((~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(B_95)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97)))) | (~tptp_fun__E_(|'0'|, f(B_95)))) <=> ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))), ((((((((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) | (~tptp_fun__E_(|'0'|, f(B_94)))) | (~iLEQ(suc(A_2), suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(suc(B_95))))) | (~tptp_fun__E_(|'0'|, f(B_98)))) | (~tptp_fun__E_(|'0'|, f(B_95)))) <=> ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 (![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : (((((((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) | (~tptp_fun__E_(|'0'|, f(B_94)))) | (~iLEQ(suc(A_2), suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(suc(B_95))))) | (~tptp_fun__E_(|'0'|, f(B_98)))) | (~tptp_fun__E_(|'0'|, f(B_95)))) <=> ![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[98])).
% 0.18/0.41 tff(100,axiom,(![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : (((((((((((((((((~iLEQ(suc(B_96), suc(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_96))))) | (~iLEQ(suc(B_97), suc(B_98)))) | (~tptp_fun__E_(|'0'|, f(suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_94))))) | (~tptp_fun__E_(|'0'|, f(B_97)))) | (~iLEQ(suc(B_95), suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(B_96)))) | (~iLEQ(suc(B_94), suc(B_95)))) | (~tptp_fun__E_(|'0'|, f(suc(B_98))))) | (~tptp_fun__E_(|'0'|, f(B_94)))) | (~iLEQ(suc(A_2), suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(suc(B_95))))) | (~tptp_fun__E_(|'0'|, f(B_98)))) | (~tptp_fun__E_(|'0'|, f(B_95))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_102')).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 (![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.18/0.41 tff(102,plain,
% 0.18/0.41 (![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.18/0.41 tff(103,plain,(
% 0.18/0.41 ![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[102])).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 (![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 (((~![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(106,plain,
% 0.19/0.42 (((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(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)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))) <=> ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (((~![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(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)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (((~![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(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)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[107, 105])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 ((~![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(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)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((~![B_98: $i, B_96: $i, B_95: $i, A_2: $i, B_94: $i, B_97: $i] : ((~tptp_fun__E_(|'0'|, f(B_95))) | (~tptp_fun__E_(|'0'|, f(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_95)))) | (~iLEQ(suc(A_2), suc(B_94))) | (~tptp_fun__E_(|'0'|, f(B_94))) | (~tptp_fun__E_(|'0'|, f(suc(B_98)))) | (~iLEQ(suc(B_94), suc(B_95))) | (~tptp_fun__E_(|'0'|, f(B_96))) | (~iLEQ(suc(B_95), suc(B_96))) | (~tptp_fun__E_(|'0'|, f(B_97))) | (~tptp_fun__E_(|'0'|, f(suc(B_94)))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_97)))) | (~iLEQ(suc(B_97), suc(B_98))) | (~tptp_fun__E_(|'0'|, f(suc(B_96)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~iLEQ(suc(B_96), suc(B_97))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[110, 104, 79, 46, 94])).
% 0.19/0.42 tff(112,plain,(tptp_fun__E_(s(|'0'|), f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(113,assumption,(tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 0.19/0.42 tff(114,assumption,(tptp_fun__E_(s(|'0'|), f(z))), introduced(assumption)).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (^[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(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 (![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(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.42 tff(120,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_70')).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.19/0.42 tff(123,plain,(
% 0.19/0.42 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[122])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(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(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[127, 124, 114])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (iLEQ(suc(z), suc(z))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[128, 113])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (^[B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : refl(((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(131,plain,
% 0.19/0.42 (![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) <=> ![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) <=> ![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 (^[B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), (((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~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))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~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))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), (((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~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))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), ((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~iLEQ(suc(B_70), suc(B_71)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~iLEQ(suc(B_70), suc(B_71)))) <=> ((~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), ((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) <=> ((~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), (((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) <=> (((~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))))), rewrite((((~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), (((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), ((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), ((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), (((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~iLEQ(suc(B_69), suc(B_70)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~iLEQ(suc(B_69), suc(B_70)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), (((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~iLEQ(suc(B_72), suc(B_73)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~iLEQ(suc(B_72), suc(B_73)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) | (~iLEQ(suc(A_1), suc(B_69)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~iLEQ(suc(A_1), suc(B_69)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~iLEQ(suc(A_1), suc(B_69)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) | (~iLEQ(suc(A_1), suc(B_69)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), ((((((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) | (~iLEQ(suc(A_1), suc(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_70)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_70)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_70)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), ((((((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) | (~iLEQ(suc(A_1), suc(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_70)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) | (~iLEQ(suc(A_1), suc(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(B_72)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_72)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_72)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) | (~iLEQ(suc(A_1), suc(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(B_72)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))))), ((((((((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) | (~iLEQ(suc(A_1), suc(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))), ((((((((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) | (~iLEQ(suc(A_1), suc(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(134,plain,
% 0.19/0.45 (![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) | (~iLEQ(suc(A_1), suc(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73))))) <=> ![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[133])).
% 0.19/0.45 tff(135,axiom,(![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(B_69))) | (~iLEQ(suc(B_71), suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(B_70), suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71))))) | (~iLEQ(suc(B_69), suc(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69))))) | (~iLEQ(suc(B_72), suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70))))) | (~tptp_fun__E_(s(|'0'|), f(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72))))) | (~iLEQ(suc(A_1), suc(B_69)))) | (~tptp_fun__E_(s(|'0'|), f(B_70)))) | (~tptp_fun__E_(s(|'0'|), f(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_179')).
% 0.19/0.45 tff(136,plain,
% 0.19/0.45 (![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.45 tff(137,plain,
% 0.19/0.45 (![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.19/0.45 tff(138,plain,(
% 0.19/0.45 ![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[137])).
% 0.19/0.45 tff(139,plain,
% 0.19/0.45 (![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.19/0.45 tff(140,plain,
% 0.19/0.45 (((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(141,plain,
% 0.19/0.45 (((~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(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z)))) <=> ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(142,plain,
% 0.19/0.45 (((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | ((~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(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[141])).
% 0.19/0.45 tff(143,plain,
% 0.19/0.45 (((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | ((~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(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[142, 140])).
% 0.19/0.46 tff(144,plain,
% 0.19/0.46 ((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | ((~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(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 ((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.19/0.46 tff(146,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[145, 139, 114, 113, 129])).
% 0.19/0.46 tff(147,plain,((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(148,plain,
% 0.19/0.46 (~tptp_fun__E_(s(|'0'|), f(z))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[147, 112])).
% 0.19/0.46 tff(149,plain,
% 0.19/0.46 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(150,plain,
% 0.19/0.46 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[149, 9])).
% 0.19/0.46 tff(151,plain,
% 0.19/0.46 (((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))) <=> ((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(152,plain,
% 0.19/0.46 ((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(153,plain,
% 0.19/0.46 ((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_68)) | (~tptp_fun__LE_(f(B_68), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.46 tff(154,plain,
% 0.19/0.46 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[153, 56])).
% 0.19/0.46 tff(155,plain,
% 0.19/0.46 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[154, 150])).
% 0.19/0.46 tff(156,plain,
% 0.19/0.46 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[155, 148])).
% 0.19/0.46 tff(157,plain,
% 0.19/0.46 (tptp_fun__E_(|'0'|, f(z))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[45, 156])).
% 0.19/0.46 tff(158,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 0.19/0.46 tff(159,plain,
% 0.19/0.46 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(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(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(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))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(160,plain,
% 0.19/0.46 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(161,plain,
% 0.19/0.46 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(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)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[160])).
% 0.19/0.46 tff(162,plain,
% 0.19/0.46 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(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))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[161, 159])).
% 0.19/0.46 tff(163,plain,
% 0.19/0.46 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(164,plain,
% 0.19/0.46 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.19/0.46 tff(165,plain,
% 0.19/0.46 (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[164, 124, 112])).
% 0.19/0.46 tff(166,plain,
% 0.19/0.46 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[165, 158])).
% 0.19/0.46 tff(167,plain,
% 0.19/0.46 (((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | ((~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_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(168,plain,
% 0.19/0.46 (((~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(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~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(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))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(169,plain,
% 0.19/0.46 (((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | ((~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(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~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(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)))))) <=> ((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.46 tff(170,plain,
% 0.19/0.46 (((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | ((~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(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~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(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)))))) <=> ((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[169, 167])).
% 0.19/0.46 tff(171,plain,
% 0.19/0.46 ((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | ((~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(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~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(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)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(172,plain,
% 0.19/0.47 ((~![B_73: $i, B_72: $i, A_1: $i, B_70: $i, B_69: $i, B_71: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_71)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_73)))) | (~tptp_fun__E_(s(|'0'|), f(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_70))) | (~iLEQ(suc(A_1), suc(B_69))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_72)))) | (~tptp_fun__E_(s(|'0'|), f(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_70)))) | (~iLEQ(suc(B_72), suc(B_73))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_69)))) | (~iLEQ(suc(B_69), suc(B_70))) | (~iLEQ(suc(B_70), suc(B_71))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(B_71), suc(B_72))) | (~tptp_fun__E_(s(|'0'|), f(B_69))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.47 tff(173,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[172, 139, 112, 158, 166])).
% 0.19/0.47 tff(174,plain,(~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(175,plain,
% 0.19/0.47 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(176,plain,
% 0.19/0.47 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[175, 9])).
% 0.19/0.47 tff(177,plain,
% 0.19/0.47 (((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), 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_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), 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'|)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(178,plain,
% 0.19/0.47 ((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), 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'|)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(179,plain,
% 0.19/0.47 ((~![B_68: $i] : (tptp_fun__LE_(f(B_68), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_68))) | (~tptp_fun__LE_(f(suc(B_68)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.19/0.47 tff(180,plain,
% 0.19/0.47 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[179, 22])).
% 0.19/0.47 tff(181,plain,
% 0.19/0.47 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[180, 176, 174])).
% 0.19/0.47 tff(182,plain,
% 0.19/0.47 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[78, 181])).
% 0.19/0.47 tff(183,plain,
% 0.19/0.47 (iLEQ(suc(z), suc(z))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[93, 182, 157])).
% 0.19/0.47 tff(184,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[110, 104, 182, 157, 183])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------