%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO664-1 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:42:03 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYO664-1 : TPTP v9.0.0. Released v7.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 13:23:47 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(iLEQ_type, type, (
% 0.13/0.39 iLEQ: ( $i * $i ) > $o)).
% 0.13/0.39 tff(suc_type, type, (
% 0.13/0.39 suc: $i > $i)).
% 0.13/0.39 tff(z_type, type, (
% 0.13/0.39 z: $i)).
% 0.13/0.39 tff(tptp_fun__E__type, type, (
% 0.13/0.39 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.13/0.39 tff(f_type, type, (
% 0.13/0.39 f: $i > $i)).
% 0.13/0.39 tff(s_type, type, (
% 0.13/0.39 s: $i > $i)).
% 0.13/0.39 tff(tptp_fun__0__type, type, (
% 0.13/0.39 tptp_fun__0_: $i)).
% 0.13/0.39 tff(tptp_fun__LE__type, type, (
% 0.13/0.39 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,assumption,(tptp_fun__E_(|'0'|, f(suc(z)))), introduced(assumption)).
% 0.13/0.39 tff(2,assumption,(~tptp_fun__LE_(f(z), s(|'0'|))), introduced(assumption)).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(s(|'0'|))) <=> tptp_fun__LE_(f(A), s(s(|'0'|))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(6,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_58')).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.13/0.39 tff(8,plain,(
% 0.13/0.39 ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[7])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[10, 9])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (^[B_42: $i] : refl((tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))) <=> (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))) <=> ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[12])).
% 0.13/0.39 tff(14,plain,
% 0.13/0.39 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))) <=> ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(15,plain,
% 0.13/0.39 (^[B_42: $i] : rewrite((((~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))) | tptp_fun__LE_(f(B_42), s(|'0'|))) <=> (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(16,plain,
% 0.13/0.39 (![B_42: $i] : (((~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))) | tptp_fun__LE_(f(B_42), s(|'0'|))) <=> ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[15])).
% 0.13/0.39 tff(17,axiom,(![B_42: $i] : (((~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42))) | tptp_fun__LE_(f(B_42), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_20')).
% 0.13/0.39 tff(18,plain,
% 0.13/0.39 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.13/0.39 tff(19,plain,
% 0.13/0.39 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.13/0.39 tff(20,plain,(
% 0.13/0.39 ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 0.13/0.39 inference(skolemize,[status(sab)],[19])).
% 0.13/0.39 tff(21,plain,
% 0.13/0.39 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.13/0.39 tff(22,plain,
% 0.13/0.39 (((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))) <=> ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(23,plain,
% 0.13/0.39 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(24,plain,
% 0.13/0.39 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.13/0.39 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.39 tff(25,plain,
% 0.13/0.39 (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.13/0.39 tff(26,plain,
% 0.13/0.39 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[25, 11])).
% 0.13/0.39 tff(27,plain,
% 0.13/0.39 (tptp_fun__E_(s(|'0'|), f(z))),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[26, 2])).
% 0.13/0.39 tff(28,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 0.13/0.39 tff(29,plain,
% 0.13/0.39 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 0.13/0.39 inference(quant_inst,[status(thm)],[])).
% 0.13/0.39 tff(30,plain,
% 0.13/0.39 ($false),
% 0.13/0.39 inference(unit_resolution,[status(thm)],[29, 9, 28])).
% 0.13/0.39 tff(31,plain,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.13/0.39 tff(32,plain,
% 0.13/0.39 (^[B_42: $i] : refl((tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(33,plain,
% 0.13/0.39 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|))))) <=> ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[32])).
% 0.13/0.39 tff(34,plain,
% 0.13/0.39 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|))))) <=> ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.39 tff(35,plain,
% 0.13/0.39 (^[B_42: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_42)))) | tptp_fun__LE_(f(B_42), s(|'0'|))) <=> (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(36,plain,
% 0.13/0.39 (![B_42: $i] : (((~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_42)))) | tptp_fun__LE_(f(B_42), s(|'0'|))) <=> ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.13/0.39 tff(37,axiom,(![B_42: $i] : (((~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_42)))) | tptp_fun__LE_(f(B_42), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_83')).
% 0.21/0.39 tff(38,plain,
% 0.21/0.39 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.39 tff(39,plain,
% 0.21/0.39 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.21/0.39 tff(40,plain,(
% 0.21/0.39 ![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 0.21/0.39 inference(skolemize,[status(sab)],[39])).
% 0.21/0.39 tff(41,plain,
% 0.21/0.39 (![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.21/0.39 tff(42,plain,
% 0.21/0.39 (((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(43,plain,
% 0.21/0.39 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(44,plain,
% 0.21/0.39 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.21/0.39 tff(45,plain,
% 0.21/0.39 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[44, 41])).
% 0.21/0.39 tff(46,plain,
% 0.21/0.39 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[45, 2, 31])).
% 0.21/0.39 tff(47,plain,
% 0.21/0.39 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(48,plain,
% 0.21/0.39 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.39 tff(49,plain,
% 0.21/0.39 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(50,plain,
% 0.21/0.39 (^[A_1: $i] : rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(51,plain,
% 0.21/0.39 (![A_1: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.39 tff(52,axiom,(![A_1: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_50')).
% 0.21/0.39 tff(53,plain,
% 0.21/0.39 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.40 tff(54,plain,
% 0.21/0.40 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.21/0.40 tff(55,plain,(
% 0.21/0.40 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[54])).
% 0.21/0.40 tff(56,plain,
% 0.21/0.40 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.21/0.40 tff(57,plain,
% 0.21/0.40 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(58,plain,
% 0.21/0.40 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(59,plain,
% 0.21/0.40 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.21/0.40 tff(60,plain,
% 0.21/0.40 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.21/0.40 tff(61,plain,
% 0.21/0.40 (iLEQ(suc(z), suc(z))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[60, 46, 27])).
% 0.21/0.40 tff(62,plain,
% 0.21/0.40 (^[B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : refl(((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(63,plain,
% 0.21/0.40 (![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) <=> ![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[62])).
% 0.21/0.40 tff(64,plain,
% 0.21/0.40 (![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) <=> ![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(65,plain,
% 0.21/0.40 (^[B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(A_1), suc(B_43)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(A_1), suc(B_43)))) <=> ((~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) <=> ((~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) <=> (((~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))))), rewrite((((~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(B_44), suc(B_45)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(B_44), suc(B_45)))) <=> ((~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) <=> ((~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) <=> (((~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))))), rewrite((((~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(B_45), suc(B_46)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(B_45), suc(B_46)))) <=> ((~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) <=> ((~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) | (~iLEQ(suc(B_43), suc(B_44)))) <=> (((~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(B_43), suc(B_44)))))), rewrite((((~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~iLEQ(suc(B_43), suc(B_44)))) <=> ((~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) | (~iLEQ(suc(B_43), suc(B_44)))) <=> ((~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) | (~iLEQ(suc(B_43), suc(B_44)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_44))))) <=> (((~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_44))))))), rewrite((((~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_44))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) | (~iLEQ(suc(B_43), suc(B_44)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_44))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(66,plain,
% 0.21/0.42 (![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) | (~iLEQ(suc(B_43), suc(B_44)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_44))))) <=> ![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.42 tff(67,axiom,(![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(B_43)))) | (~iLEQ(suc(B_44), suc(B_45)))) | (~tptp_fun__E_(s(|'0'|), f(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_44)))) | (~iLEQ(suc(B_45), suc(B_46)))) | (~iLEQ(suc(B_43), suc(B_44)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_44)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_37')).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 (![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.21/0.42 tff(70,plain,(
% 0.21/0.42 ![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[69])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 (((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 (((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[73])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[74, 72])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[77, 71, 46, 27, 61])).
% 0.21/0.42 tff(79,plain,(tptp_fun__LE_(f(z), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 (^[B_60: $i] : refl(((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60))) <=> ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60))) <=> ![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[80])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60))) <=> ![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (^[B_60: $i] : rewrite((((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_60))) | tptp_fun__LE_(f(B_60), |'0'|)) <=> ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (![B_60: $i] : (((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_60))) | tptp_fun__LE_(f(B_60), |'0'|)) <=> ![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.42 tff(85,axiom,(![B_60: $i] : (((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_60))) | tptp_fun__LE_(f(B_60), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_94')).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.42 tff(87,plain,
% 0.21/0.42 (![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.21/0.42 tff(88,plain,(
% 0.21/0.42 ![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[87])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.21/0.42 tff(90,plain,
% 0.21/0.42 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(91,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_70')).
% 0.21/0.42 tff(92,plain,
% 0.21/0.43 (~tptp_fun__LE_(f(z), |'0'|)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 (((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(94,plain,
% 0.21/0.43 (((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z))) <=> (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[94])).
% 0.21/0.43 tff(96,plain,
% 0.21/0.43 (((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[95, 93])).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 ((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 ((~![B_60: $i] : ((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__LE_(f(B_60), |'0'|) | tptp_fun__E_(|'0'|, f(B_60)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[98, 92, 89])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 (tptp_fun__E_(|'0'|, f(z))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[99, 79])).
% 0.21/0.43 tff(101,plain,
% 0.21/0.43 (^[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))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (![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)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[101])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 (![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)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 (^[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))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 (![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)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.43 tff(106,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/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.21/0.43 tff(107,plain,
% 0.21/0.43 (![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)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.21/0.43 tff(108,plain,
% 0.21/0.43 (![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)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.21/0.43 tff(109,plain,(
% 0.21/0.43 ![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)))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[108])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 (![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)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 (((~![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)))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(112,plain,
% 0.21/0.43 ((~![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)))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(113,plain,
% 0.21/0.43 ((~![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))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[113, 110])).
% 0.21/0.43 tff(115,plain,
% 0.21/0.43 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[114, 100])).
% 0.21/0.43 tff(116,plain,
% 0.21/0.43 (iLEQ(suc(z), suc(z))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[115, 1])).
% 0.21/0.43 tff(117,plain,
% 0.21/0.43 (^[B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : refl(((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) <=> ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(118,plain,
% 0.21/0.43 (![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) <=> ![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[117])).
% 0.21/0.43 tff(119,plain,
% 0.21/0.43 (![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) <=> ![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(120,plain,
% 0.21/0.43 (^[B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(A_2), suc(B_61)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(A_2), suc(B_61)))) <=> ((~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) <=> ((~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), ((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) <=> (((~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(B_61), suc(B_62)))))), rewrite((((~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(B_61), suc(B_62)))) <=> ((~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), ((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) <=> ((~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), (((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) <=> (((~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))))), rewrite((((~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), ((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(A_2)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), ((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), (((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) <=> (((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(B_62), suc(B_63)))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(B_62), suc(B_63)))) <=> ((~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) <=> ((~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), ((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) <=> (((~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))))), rewrite((((~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) <=> ((~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), ((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) <=> ((~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), (((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) <=> (((~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(B_63), suc(B_64)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~iLEQ(suc(B_63), suc(B_64)))) <=> ((~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) <=> ((~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), ((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) <=> (((~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))))), rewrite((((~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), ((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), (((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_61)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_61)))) <=> ((~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) <=> ((~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) <=> (((~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) | (~tptp_fun__E_(|'0'|, f(B_62)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_62)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_62)))) <=> ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) | (~tptp_fun__E_(|'0'|, f(B_62)))) <=> ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) | (~tptp_fun__E_(|'0'|, f(B_62)))) <=> ![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[120])).
% 0.21/0.45 tff(122,axiom,(![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((((((((((((((~tptp_fun__E_(|'0'|, f(B_63))) | (~tptp_fun__E_(|'0'|, f(suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~tptp_fun__E_(|'0'|, f(suc(B_63))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(B_62), suc(B_63)))) | (~tptp_fun__E_(|'0'|, f(B_64)))) | (~iLEQ(suc(B_63), suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_64))))) | (~tptp_fun__E_(|'0'|, f(B_62))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_66')).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 (![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 (![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.21/0.45 tff(125,plain,(
% 0.21/0.45 ![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[124])).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 (![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 (((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 (((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))) <=> ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 (((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))) <=> ((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[128])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 (((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))) <=> ((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[129, 127])).
% 0.21/0.45 tff(131,plain,
% 0.21/0.45 ((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 ((~![B_63: $i, B_64: $i, B_62: $i, B_61: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_64)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(B_63), suc(B_64))) | (~tptp_fun__E_(|'0'|, f(B_64))) | (~iLEQ(suc(B_62), suc(B_63))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_63)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_2), suc(B_61))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_63))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.45 tff(133,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[132, 126, 100, 1, 116])).
% 0.21/0.45 tff(134,plain,(~tptp_fun__E_(|'0'|, f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(135,plain,
% 0.21/0.45 (^[B_60: $i] : refl((tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) <=> (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(136,plain,
% 0.21/0.45 (![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) <=> ![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[135])).
% 0.21/0.45 tff(137,plain,
% 0.21/0.45 (![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) <=> ![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(138,plain,
% 0.21/0.45 (^[B_60: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) | tptp_fun__LE_(f(B_60), |'0'|)) <=> (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(139,plain,
% 0.21/0.45 (![B_60: $i] : (((~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) | tptp_fun__LE_(f(B_60), |'0'|)) <=> ![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[138])).
% 0.21/0.46 tff(140,axiom,(![B_60: $i] : (((~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) | tptp_fun__LE_(f(B_60), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_117')).
% 0.21/0.46 tff(141,plain,
% 0.21/0.46 (![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.21/0.46 tff(142,plain,
% 0.21/0.46 (![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.21/0.46 tff(143,plain,(
% 0.21/0.46 ![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[142])).
% 0.21/0.46 tff(144,plain,
% 0.21/0.46 (![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[143, 136])).
% 0.21/0.46 tff(145,plain,
% 0.21/0.46 (((~![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(146,plain,
% 0.21/0.46 ((~![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(147,plain,
% 0.21/0.46 ((~![B_60: $i] : (tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.21/0.46 tff(148,plain,
% 0.21/0.46 ((~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[147, 92, 144])).
% 0.21/0.46 tff(149,plain,
% 0.21/0.46 (~tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[148, 134])).
% 0.21/0.46 tff(150,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), introduced(assumption)).
% 0.21/0.46 tff(151,plain,
% 0.21/0.46 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[151, 9, 150])).
% 0.21/0.46 tff(153,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 (((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))) <=> ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(155,plain,
% 0.21/0.46 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_42))) | (~tptp_fun__LE_(f(suc(B_42)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.21/0.46 tff(157,plain,
% 0.21/0.46 (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'|))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[156, 41])).
% 0.21/0.46 tff(158,plain,
% 0.21/0.46 (tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[157, 153, 149])).
% 0.21/0.46 tff(159,plain,
% 0.21/0.46 (((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))) <=> ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(160,plain,
% 0.21/0.46 ((tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))) <=> (tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 (((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[160])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 (((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.21/0.46 inference(transitivity,[status(thm)],[161, 159])).
% 0.21/0.46 tff(163,plain,
% 0.21/0.46 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(164,plain,
% 0.21/0.46 ((~![B_42: $i] : (tptp_fun__LE_(f(B_42), s(|'0'|)) | (~tptp_fun__LE_(f(B_42), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_42)))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.21/0.46 tff(165,plain,
% 0.21/0.46 (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[164, 21, 31])).
% 0.21/0.46 tff(166,plain,
% 0.21/0.46 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[165, 149])).
% 0.21/0.46 tff(167,plain,
% 0.21/0.46 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(168,plain,
% 0.21/0.46 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(169,plain,
% 0.21/0.46 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[168])).
% 0.21/0.46 tff(170,plain,
% 0.21/0.46 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[169, 167])).
% 0.21/0.46 tff(171,plain,
% 0.21/0.46 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(172,plain,
% 0.21/0.46 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.21/0.46 tff(173,plain,
% 0.21/0.46 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[172, 56, 166, 158])).
% 0.21/0.46 tff(174,plain,
% 0.21/0.46 (((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(175,plain,
% 0.21/0.46 (((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(176,plain,
% 0.21/0.46 (((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[175])).
% 0.21/0.46 tff(177,plain,
% 0.21/0.46 (((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[176, 174])).
% 0.21/0.47 tff(178,plain,
% 0.21/0.47 ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(179,plain,
% 0.21/0.47 ((~![B_43: $i, B_46: $i, B_45: $i, A_1: $i, B_44: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_44)))) | (~iLEQ(suc(B_43), suc(B_44))) | (~iLEQ(suc(B_45), suc(B_46))) | (~tptp_fun__E_(s(|'0'|), f(B_44))) | (~tptp_fun__E_(s(|'0'|), f(B_46))) | (~iLEQ(suc(B_44), suc(B_45))) | (~tptp_fun__E_(s(|'0'|), f(B_43))) | (~iLEQ(suc(A_1), suc(B_43))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_43)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_46)))) | (~tptp_fun__E_(s(|'0'|), f(B_45))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_45)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[179, 71, 166, 158, 173])).
% 0.21/0.47 % SZS output end Proof
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------