%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO674-1 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:42:05 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO674-1 : TPTP v9.0.0. Released v7.3.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 13:22:18 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.37 % SZS status Unsatisfiable
% 0.11/0.37 % SZS output start Proof
% 0.11/0.37 tff(iLEQ_type, type, (
% 0.11/0.37 iLEQ: ( $i * $i ) > $o)).
% 0.11/0.37 tff(suc_type, type, (
% 0.11/0.37 suc: $i > $i)).
% 0.11/0.37 tff(z_type, type, (
% 0.11/0.37 z: $i)).
% 0.11/0.37 tff(tptp_fun__E__type, type, (
% 0.11/0.37 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.11/0.37 tff(f_type, type, (
% 0.11/0.37 f: $i > $i)).
% 0.11/0.37 tff(tptp_fun__0__type, type, (
% 0.11/0.37 tptp_fun__0_: $i)).
% 0.11/0.37 tff(tptp_fun__LE__type, type, (
% 0.11/0.37 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.11/0.37 tff(s_type, type, (
% 0.11/0.37 s: $i > $i)).
% 0.11/0.37 tff(1,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), introduced(assumption)).
% 0.11/0.37 tff(2,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.11/0.37 tff(3,plain,
% 0.11/0.37 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(s(s(|'0'|)))) <=> tptp_fun__LE_(f(A), s(s(s(|'0'|)))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(4,plain,
% 0.11/0.37 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|)))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.37 tff(5,plain,
% 0.11/0.37 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|)))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(6,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_498')).
% 0.11/0.37 tff(7,plain,
% 0.11/0.37 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.11/0.37 tff(8,plain,(
% 0.11/0.37 ![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[7])).
% 0.11/0.37 tff(9,plain,
% 0.11/0.37 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.11/0.37 tff(10,plain,
% 0.11/0.37 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(11,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.11/0.37 tff(12,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(13,plain,
% 0.11/0.37 (^[B_158: $i] : refl((tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))))) <=> (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(14,plain,
% 0.11/0.37 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[13])).
% 0.11/0.37 tff(15,plain,
% 0.11/0.37 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(16,plain,
% 0.11/0.37 (^[B_158: $i] : rewrite((((~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_158))) | tptp_fun__LE_(f(B_158), s(s(|'0'|)))) <=> (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(17,plain,
% 0.11/0.37 (![B_158: $i] : (((~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_158))) | tptp_fun__LE_(f(B_158), s(s(|'0'|)))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[16])).
% 0.11/0.37 tff(18,axiom,(![B_158: $i] : (((~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_158))) | tptp_fun__LE_(f(B_158), s(s(|'0'|))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_139')).
% 0.11/0.37 tff(19,plain,
% 0.11/0.37 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.11/0.37 tff(20,plain,
% 0.11/0.37 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.11/0.37 tff(21,plain,(
% 0.11/0.37 ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 0.11/0.37 inference(skolemize,[status(sab)],[20])).
% 0.11/0.37 tff(22,plain,
% 0.11/0.37 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.11/0.37 tff(23,plain,
% 0.11/0.37 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(24,plain,
% 0.11/0.37 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(25,plain,
% 0.11/0.37 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.11/0.37 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.11/0.37 tff(26,plain,
% 0.11/0.37 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[25, 22, 12])).
% 0.11/0.37 tff(27,plain,
% 0.11/0.37 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[26, 1])).
% 0.11/0.37 tff(28,assumption,(~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.11/0.37 tff(29,plain,
% 0.11/0.37 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))),
% 0.11/0.37 inference(quant_inst,[status(thm)],[])).
% 0.11/0.37 tff(30,plain,
% 0.11/0.37 ($false),
% 0.11/0.37 inference(unit_resolution,[status(thm)],[29, 9, 28])).
% 0.11/0.37 tff(31,plain,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.37 tff(32,plain,
% 0.11/0.37 (^[B_158: $i] : refl((tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|)))))) <=> (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.37 tff(33,plain,
% 0.11/0.37 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|)))))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 0.11/0.37 inference(quant_intro,[status(thm)],[32])).
% 0.11/0.37 tff(34,plain,
% 0.11/0.37 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|)))))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 0.11/0.37 inference(rewrite,[status(thm)],[])).
% 0.11/0.37 tff(35,plain,
% 0.11/0.37 (^[B_158: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158)))) | tptp_fun__LE_(f(B_158), s(s(|'0'|)))) <=> (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|)))))))),
% 0.11/0.37 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (![B_158: $i] : (((~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158)))) | tptp_fun__LE_(f(B_158), s(s(|'0'|)))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[35])).
% 0.11/0.38 tff(37,axiom,(![B_158: $i] : (((~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158)))) | tptp_fun__LE_(f(B_158), s(s(|'0'|))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_129')).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.11/0.38 tff(40,plain,(
% 0.11/0.38 ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[39])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[44, 41])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[45, 31])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[46, 1])).
% 0.11/0.38 tff(48,assumption,(tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))), introduced(assumption)).
% 0.11/0.38 tff(49,assumption,(tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))), introduced(assumption)).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[50])).
% 0.11/0.38 tff(52,plain,
% 0.11/0.38 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (^[A_1: $i] : rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 (![A_1: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[53])).
% 0.11/0.38 tff(55,axiom,(![A_1: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_126')).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.11/0.38 tff(58,plain,(
% 0.11/0.38 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[57])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 ((iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[61])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))))),
% 0.11/0.38 inference(transitivity,[status(thm)],[62, 60])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[65, 59, 49])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[66, 48])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (^[B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : refl(((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) <=> ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.11/0.39 tff(70,plain,
% 0.11/0.39 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) <=> ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(71,plain,
% 0.11/0.39 (^[B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_160), suc(B_161)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_160), suc(B_161)))) <=> ((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) <=> ((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) <=> (((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))))), rewrite((((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), (((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), (((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_159), suc(B_160)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_159), suc(B_160)))) <=> ((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) <=> ((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) <=> (((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))))), rewrite((((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), (((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), (((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_161), suc(B_162)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_161), suc(B_162)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), (((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), (((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) | (~iLEQ(suc(B_162), suc(B_163)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_162), suc(B_163)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(B_162), suc(B_163)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), (((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) | (~iLEQ(suc(B_162), suc(B_163)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))))), ((((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) | (~iLEQ(suc(B_162), suc(B_163)))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(A_1), suc(B_159)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1)))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))), ((((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) | (~iLEQ(suc(B_162), suc(B_163)))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : (((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) | (~iLEQ(suc(B_162), suc(B_163)))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.41 tff(73,axiom,(![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : (((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(A_1))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160)))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159))))) | (~iLEQ(suc(B_162), suc(B_163)))) | (~iLEQ(suc(A_1), suc(B_159))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_431')).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.19/0.41 tff(76,plain,(
% 0.19/0.41 ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[75])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[79])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[80, 78])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[83, 77, 48, 49, 67])).
% 0.19/0.42 tff(85,plain,((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[85, 47, 27])).
% 0.19/0.42 tff(87,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(88,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[91, 41, 12])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[92, 88])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[94, 9])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(97,plain,
% 0.19/0.43 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[98, 22, 95])).
% 0.19/0.43 tff(100,plain,
% 0.19/0.43 (tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[99, 88])).
% 0.19/0.43 tff(101,assumption,(tptp_fun__E_(s(s(|'0'|)), f(suc(z)))), introduced(assumption)).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[103])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[104, 102])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[107, 59, 101])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[108, 48])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[111])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[112, 110])).
% 0.19/0.44 tff(114,plain,
% 0.19/0.44 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(115,plain,
% 0.19/0.44 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.44 tff(116,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[115, 77, 101, 48, 109])).
% 0.19/0.44 tff(117,plain,((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(118,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[117, 100, 93])).
% 0.19/0.44 tff(119,plain,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(120,assumption,(~tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 0.19/0.44 tff(121,plain,
% 0.19/0.44 (^[B_228: $i] : refl((tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))) <=> (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(122,plain,
% 0.19/0.44 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))) <=> ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[121])).
% 0.19/0.44 tff(123,plain,
% 0.19/0.44 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))) <=> ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(124,plain,
% 0.19/0.44 (^[B_228: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))) | tptp_fun__LE_(f(B_228), s(|'0'|))) <=> (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(125,plain,
% 0.19/0.44 (![B_228: $i] : (((~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))) | tptp_fun__LE_(f(B_228), s(|'0'|))) <=> ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[124])).
% 0.19/0.44 tff(126,axiom,(![B_228: $i] : (((~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228)))) | tptp_fun__LE_(f(B_228), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_84')).
% 0.19/0.44 tff(127,plain,
% 0.19/0.44 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.19/0.44 tff(128,plain,
% 0.19/0.44 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.19/0.44 tff(129,plain,(
% 0.19/0.44 ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[128])).
% 0.19/0.44 tff(130,plain,
% 0.19/0.44 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.19/0.44 tff(131,plain,
% 0.19/0.44 (((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(132,plain,
% 0.19/0.44 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(133,plain,
% 0.19/0.44 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.19/0.44 tff(134,plain,
% 0.19/0.44 (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[133, 130])).
% 0.19/0.44 tff(135,plain,
% 0.19/0.44 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[134, 120, 119])).
% 0.19/0.44 tff(136,plain,
% 0.19/0.44 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(137,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_204')).
% 0.19/0.44 tff(138,plain,
% 0.19/0.44 (~tptp_fun__LE_(f(z), |'0'|)),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.44 tff(139,plain,
% 0.19/0.44 (^[B_253: $i] : refl(((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253))) <=> ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(140,plain,
% 0.19/0.44 (![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253))) <=> ![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[139])).
% 0.19/0.44 tff(141,plain,
% 0.19/0.44 (![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253))) <=> ![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(142,plain,
% 0.19/0.44 (^[B_253: $i] : rewrite((((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_253))) | tptp_fun__LE_(f(B_253), |'0'|)) <=> ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(143,plain,
% 0.19/0.44 (![B_253: $i] : (((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_253))) | tptp_fun__LE_(f(B_253), |'0'|)) <=> ![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[142])).
% 0.19/0.44 tff(144,axiom,(![B_253: $i] : (((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_253))) | tptp_fun__LE_(f(B_253), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_176')).
% 0.19/0.44 tff(145,plain,
% 0.19/0.44 (![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.19/0.44 tff(146,plain,
% 0.19/0.44 (![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.19/0.44 tff(147,plain,(
% 0.19/0.44 ![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 0.19/0.44 inference(skolemize,[status(sab)],[146])).
% 0.19/0.44 tff(148,plain,
% 0.19/0.44 (![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.19/0.44 tff(149,plain,
% 0.19/0.44 (((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(150,plain,
% 0.19/0.44 (((~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)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(151,plain,
% 0.19/0.44 (((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[150])).
% 0.19/0.45 tff(152,plain,
% 0.19/0.45 (((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[151, 149])).
% 0.19/0.45 tff(153,plain,
% 0.19/0.45 ((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(154,plain,
% 0.19/0.45 ((~![B_253: $i] : ((~tptp_fun__LE_(f(B_253), s(|'0'|))) | tptp_fun__LE_(f(B_253), |'0'|) | tptp_fun__E_(|'0'|, f(B_253)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.45 tff(155,plain,
% 0.19/0.45 ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[154, 148, 138])).
% 0.19/0.45 tff(156,plain,
% 0.19/0.45 (tptp_fun__E_(|'0'|, f(z))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[155, 135])).
% 0.19/0.45 tff(157,plain,
% 0.19/0.45 (^[B_228: $i] : refl((tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))) <=> (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(158,plain,
% 0.19/0.45 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))) <=> ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[157])).
% 0.19/0.45 tff(159,plain,
% 0.19/0.45 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))) <=> ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(160,plain,
% 0.19/0.45 (^[B_228: $i] : rewrite((((~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))) | tptp_fun__LE_(f(B_228), s(|'0'|))) <=> (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(161,plain,
% 0.19/0.45 (![B_228: $i] : (((~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))) | tptp_fun__LE_(f(B_228), s(|'0'|))) <=> ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[160])).
% 0.19/0.45 tff(162,axiom,(![B_228: $i] : (((~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228))) | tptp_fun__LE_(f(B_228), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_298')).
% 0.19/0.45 tff(163,plain,
% 0.19/0.45 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.19/0.45 tff(164,plain,
% 0.19/0.45 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.19/0.45 tff(165,plain,(
% 0.19/0.45 ![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 0.19/0.45 inference(skolemize,[status(sab)],[164])).
% 0.19/0.45 tff(166,plain,
% 0.19/0.45 (![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.19/0.45 tff(167,plain,
% 0.19/0.45 (((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | ((~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))) <=> ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(168,plain,
% 0.19/0.45 ((tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))) <=> ((~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(169,plain,
% 0.19/0.45 (((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | ((~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.45 tff(170,plain,
% 0.19/0.45 (((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[169, 167])).
% 0.19/0.45 tff(171,plain,
% 0.19/0.45 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(172,plain,
% 0.19/0.45 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.19/0.45 tff(173,plain,
% 0.19/0.45 (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[172, 166, 119])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[173, 120])).
% 0.19/0.45 tff(175,plain,
% 0.19/0.45 (^[B_253: $i] : refl((tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))) <=> (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(176,plain,
% 0.19/0.45 (![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))) <=> ![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[175])).
% 0.19/0.45 tff(177,plain,
% 0.19/0.45 (![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))) <=> ![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(178,plain,
% 0.19/0.45 (^[B_253: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))) | tptp_fun__LE_(f(B_253), |'0'|)) <=> (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(179,plain,
% 0.19/0.45 (![B_253: $i] : (((~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))) | tptp_fun__LE_(f(B_253), |'0'|)) <=> ![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[178])).
% 0.19/0.45 tff(180,axiom,(![B_253: $i] : (((~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253)))) | tptp_fun__LE_(f(B_253), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_50')).
% 0.19/0.45 tff(181,plain,
% 0.19/0.45 (![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.19/0.45 tff(182,plain,
% 0.19/0.45 (![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.19/0.45 tff(183,plain,(
% 0.19/0.45 ![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[182])).
% 0.19/0.45 tff(184,plain,
% 0.19/0.45 (![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[183, 176])).
% 0.19/0.45 tff(185,plain,
% 0.19/0.45 (((~![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(186,plain,
% 0.19/0.45 ((~![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(187,plain,
% 0.19/0.45 ((~![B_253: $i] : (tptp_fun__LE_(f(B_253), |'0'|) | (~tptp_fun__LE_(f(suc(B_253)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_253))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.45 tff(188,plain,
% 0.19/0.45 ((~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[187, 138, 184])).
% 0.19/0.45 tff(189,plain,
% 0.19/0.45 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[188, 174])).
% 0.19/0.45 tff(190,plain,
% 0.19/0.45 (^[A_3: $i] : refl((iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(191,plain,
% 0.19/0.45 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[190])).
% 0.19/0.45 tff(192,plain,
% 0.19/0.45 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(193,plain,
% 0.19/0.45 (^[A_3: $i] : rewrite((((~tptp_fun__E_(|'0'|, f(A_3))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | iLEQ(suc(A_3), suc(A_3))) <=> (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(194,plain,
% 0.19/0.45 (![A_3: $i] : (((~tptp_fun__E_(|'0'|, f(A_3))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | iLEQ(suc(A_3), suc(A_3))) <=> ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[193])).
% 0.19/0.45 tff(195,axiom,(![A_3: $i] : (((~tptp_fun__E_(|'0'|, f(A_3))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | iLEQ(suc(A_3), suc(A_3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_281')).
% 0.19/0.45 tff(196,plain,
% 0.19/0.45 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.19/0.45 tff(197,plain,
% 0.19/0.45 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.19/0.45 tff(198,plain,(
% 0.19/0.45 ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[197])).
% 0.19/0.45 tff(199,plain,
% 0.19/0.45 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.19/0.45 tff(200,plain,
% 0.19/0.45 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))) <=> ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(201,plain,
% 0.19/0.45 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(202,plain,
% 0.19/0.45 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(A_3))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.19/0.45 tff(203,plain,
% 0.19/0.45 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[202, 199])).
% 0.19/0.45 tff(204,plain,
% 0.19/0.45 (iLEQ(suc(z), suc(z))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[203, 189, 156])).
% 0.19/0.45 tff(205,plain,
% 0.19/0.45 (^[B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : refl(((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(206,plain,
% 0.19/0.45 (![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) <=> ![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[205])).
% 0.19/0.46 tff(207,plain,
% 0.19/0.46 (![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) <=> ![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(208,plain,
% 0.19/0.46 (^[B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_255), suc(B_256)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_255), suc(B_256)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_258)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_256), suc(B_257)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_256), suc(B_257)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(A_3)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_255)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) <=> ((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) <=> (((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_254), suc(B_255)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_254), suc(B_255)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_257), suc(B_258)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~iLEQ(suc(B_257), suc(B_258)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), (((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) | (~tptp_fun__E_(|'0'|, f(B_256)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_256)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_256)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), (((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) | (~tptp_fun__E_(|'0'|, f(B_256)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))))), ((((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) | (~tptp_fun__E_(|'0'|, f(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_257)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_257)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_257)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))), ((((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) | (~tptp_fun__E_(|'0'|, f(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_257)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(209,plain,
% 0.19/0.47 (![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : (((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) | (~tptp_fun__E_(|'0'|, f(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_257)))) <=> ![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[208])).
% 0.19/0.47 tff(210,axiom,(![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : (((((((((((((((((~iLEQ(suc(A_3), suc(B_254))) | (~tptp_fun__E_(|'0'|, f(B_254)))) | (~tptp_fun__E_(|'0'|, f(suc(B_257))))) | (~iLEQ(suc(B_255), suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_258)))) | (~iLEQ(suc(B_256), suc(B_257)))) | (~tptp_fun__E_(|'0'|, f(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(B_254))))) | (~iLEQ(suc(B_254), suc(B_255)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3))))) | (~tptp_fun__E_(|'0'|, f(suc(B_256))))) | (~iLEQ(suc(B_257), suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255))))) | (~tptp_fun__E_(|'0'|, f(suc(B_258))))) | (~tptp_fun__E_(|'0'|, f(B_256)))) | (~tptp_fun__E_(|'0'|, f(B_257))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_453')).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 (![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.19/0.47 tff(212,plain,
% 0.19/0.47 (![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.19/0.47 tff(213,plain,(
% 0.19/0.47 ![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[212])).
% 0.19/0.47 tff(214,plain,
% 0.19/0.47 (![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.19/0.47 tff(215,plain,
% 0.19/0.47 (((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(216,plain,
% 0.19/0.47 (((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(217,plain,
% 0.19/0.47 (((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[216])).
% 0.19/0.47 tff(218,plain,
% 0.19/0.47 (((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[217, 215])).
% 0.19/0.47 tff(219,plain,
% 0.19/0.47 ((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(220,plain,
% 0.19/0.48 ((~![B_256: $i, B_255: $i, A_3: $i, B_257: $i, B_258: $i, B_254: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_254)))) | (~tptp_fun__E_(|'0'|, f(B_254))) | (~iLEQ(suc(B_254), suc(B_255))) | (~tptp_fun__E_(|'0'|, f(B_257))) | (~tptp_fun__E_(|'0'|, f(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_258)))) | (~tptp_fun__E_(|'0'|, f(suc(B_255)))) | (~iLEQ(suc(B_257), suc(B_258))) | (~tptp_fun__E_(|'0'|, f(suc(B_256)))) | (~tptp_fun__E_(|'0'|, f(suc(A_3)))) | (~tptp_fun__E_(|'0'|, f(B_255))) | (~tptp_fun__E_(|'0'|, f(A_3))) | (~iLEQ(suc(B_256), suc(B_257))) | (~tptp_fun__E_(|'0'|, f(B_258))) | (~iLEQ(suc(B_255), suc(B_256))) | (~tptp_fun__E_(|'0'|, f(suc(B_257)))) | (~iLEQ(suc(A_3), suc(B_254))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.19/0.48 tff(221,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[220, 214, 189, 156, 204])).
% 0.19/0.48 tff(222,plain,(tptp_fun__E_(s(|'0'|), f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(223,assumption,(tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 0.19/0.48 tff(224,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 0.19/0.48 tff(225,plain,
% 0.19/0.48 (^[A_2: $i] : refl((iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(226,plain,
% 0.19/0.48 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[225])).
% 0.19/0.48 tff(227,plain,
% 0.19/0.48 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(228,plain,
% 0.19/0.48 (^[A_2: $i] : rewrite((((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(229,plain,
% 0.19/0.48 (![A_2: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[228])).
% 0.19/0.48 tff(230,axiom,(![A_2: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_493')).
% 0.19/0.48 tff(231,plain,
% 0.19/0.48 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.19/0.48 tff(232,plain,
% 0.19/0.48 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.19/0.48 tff(233,plain,(
% 0.19/0.48 ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[232])).
% 0.19/0.48 tff(234,plain,
% 0.19/0.48 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[233, 226])).
% 0.19/0.48 tff(235,plain,
% 0.19/0.48 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(236,plain,
% 0.19/0.48 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(237,plain,
% 0.19/0.48 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[236])).
% 0.19/0.48 tff(238,plain,
% 0.19/0.48 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[237, 235])).
% 0.19/0.48 tff(239,plain,
% 0.19/0.48 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(240,plain,
% 0.19/0.48 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.19/0.48 tff(241,plain,
% 0.19/0.48 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[240, 234])).
% 0.19/0.48 tff(242,plain,
% 0.19/0.48 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[241, 224, 223])).
% 0.19/0.48 tff(243,plain,
% 0.19/0.48 (^[B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : refl(((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) <=> ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(244,plain,
% 0.19/0.48 (![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) <=> ![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[243])).
% 0.19/0.48 tff(245,plain,
% 0.19/0.48 (![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) <=> ![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(246,plain,
% 0.19/0.48 (^[B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) <=> ((~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) <=> (((~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))))), rewrite((((~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(A_2), suc(B_229)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(A_2), suc(B_229)))) <=> ((~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) <=> ((~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) <=> (((~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(B_229), suc(B_230)))))), rewrite((((~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(B_229), suc(B_230)))) <=> ((~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) <=> ((~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) <=> (((~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))))), rewrite((((~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(B_232), suc(B_233)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(B_232), suc(B_233)))) <=> ((~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) <=> ((~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) <=> (((~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))))), rewrite((((~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))))), ((((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) | (~iLEQ(suc(B_231), suc(B_232)))) <=> (((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(B_231), suc(B_232)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233))))) | (~iLEQ(suc(B_231), suc(B_232)))) <=> ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))), ((((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) | (~iLEQ(suc(B_231), suc(B_232)))) <=> ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(247,plain,
% 0.19/0.49 (![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) | (~iLEQ(suc(B_231), suc(B_232)))) <=> ![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[246])).
% 0.19/0.49 tff(248,axiom,(![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232))))) | (~iLEQ(suc(B_230), suc(B_231)))) | (~tptp_fun__E_(s(|'0'|), f(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229))))) | (~tptp_fun__E_(s(|'0'|), f(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(B_231)))) | (~iLEQ(suc(A_2), suc(B_229)))) | (~iLEQ(suc(B_229), suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231))))) | (~tptp_fun__E_(s(|'0'|), f(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230))))) | (~iLEQ(suc(B_232), suc(B_233)))) | (~tptp_fun__E_(s(|'0'|), f(A_2)))) | (~iLEQ(suc(B_231), suc(B_232))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_193')).
% 0.19/0.49 tff(249,plain,
% 0.19/0.49 (![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.19/0.49 tff(250,plain,
% 0.19/0.49 (![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[249, 245])).
% 0.19/0.49 tff(251,plain,(
% 0.19/0.49 ![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[250])).
% 0.19/0.49 tff(252,plain,
% 0.19/0.49 (![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[251, 244])).
% 0.19/0.49 tff(253,plain,
% 0.19/0.49 (((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(254,plain,
% 0.19/0.50 (((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(255,plain,
% 0.19/0.50 (((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[254])).
% 0.19/0.50 tff(256,plain,
% 0.19/0.50 (((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[255, 253])).
% 0.19/0.50 tff(257,plain,
% 0.19/0.50 ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(258,plain,
% 0.19/0.50 ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.19/0.50 tff(259,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[258, 252, 223, 224, 242])).
% 0.19/0.50 tff(260,plain,((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(261,plain,
% 0.19/0.50 (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[260, 222])).
% 0.19/0.50 tff(262,plain,
% 0.19/0.50 (((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(263,plain,
% 0.19/0.50 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(264,plain,
% 0.19/0.50 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_228)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_228))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.19/0.50 tff(265,plain,
% 0.19/0.50 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[264, 130])).
% 0.19/0.50 tff(266,plain,
% 0.19/0.50 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[265, 261])).
% 0.19/0.50 tff(267,plain,
% 0.19/0.50 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[266, 87])).
% 0.19/0.50 tff(268,plain,
% 0.19/0.50 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[188, 267])).
% 0.19/0.50 tff(269,assumption,(~tptp_fun__LE_(f(z), s(s(|'0'|)))), introduced(assumption)).
% 0.19/0.50 tff(270,plain,
% 0.19/0.50 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(271,plain,
% 0.19/0.50 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(272,plain,
% 0.19/0.50 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_158))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.19/0.50 tff(273,plain,
% 0.19/0.50 (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[272, 41])).
% 0.19/0.50 tff(274,plain,
% 0.19/0.50 (tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[273, 269, 95])).
% 0.19/0.50 tff(275,plain,
% 0.19/0.50 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(|'0'|))))) | tptp_fun__LE_(f(z), s(s(s(|'0'|))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(276,plain,
% 0.19/0.50 (tptp_fun__LE_(f(z), s(s(s(|'0'|))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[275, 9])).
% 0.19/0.50 tff(277,plain,
% 0.19/0.50 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(278,plain,
% 0.19/0.50 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(279,plain,
% 0.19/0.50 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_158)) | (~tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.19/0.50 tff(280,plain,
% 0.19/0.50 (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[279, 22, 276])).
% 0.19/0.50 tff(281,plain,
% 0.19/0.50 (tptp_fun__E_(s(s(|'0'|)), f(z))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[280, 269])).
% 0.19/0.50 tff(282,plain,
% 0.19/0.50 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(283,plain,
% 0.19/0.50 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(284,plain,
% 0.19/0.50 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.19/0.50 tff(285,plain,
% 0.19/0.50 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[284, 59])).
% 0.19/0.50 tff(286,plain,
% 0.19/0.50 (iLEQ(suc(z), suc(z))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[285, 281, 274])).
% 0.19/0.50 tff(287,plain,
% 0.19/0.50 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(288,plain,
% 0.19/0.50 (((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(289,plain,
% 0.19/0.50 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[288])).
% 0.19/0.51 tff(290,plain,
% 0.19/0.51 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[289, 287])).
% 0.19/0.51 tff(291,plain,
% 0.19/0.51 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(292,plain,
% 0.19/0.51 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_163: $i, B_161: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_161)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_161))) | (~iLEQ(suc(B_161), suc(B_162))) | (~iLEQ(suc(B_159), suc(B_160))) | (~iLEQ(suc(A_1), suc(B_159))) | (~iLEQ(suc(B_162), suc(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_159)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_160))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_162)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_160)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_163))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_162))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_1)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_159))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_163)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_1))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.19/0.51 tff(293,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[292, 77, 274, 281, 286])).
% 0.19/0.51 tff(294,plain,(tptp_fun__LE_(f(z), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(295,assumption,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 0.19/0.51 tff(296,assumption,(~tptp_fun__LE_(f(z), s(|'0'|))), introduced(assumption)).
% 0.19/0.51 tff(297,plain,
% 0.19/0.51 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[134, 296, 295])).
% 0.19/0.51 tff(298,assumption,(tptp_fun__LE_(f(z), s(s(|'0'|)))), introduced(assumption)).
% 0.19/0.51 tff(299,plain,
% 0.19/0.51 (((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))) <=> ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(300,plain,
% 0.19/0.51 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(301,plain,
% 0.19/0.51 ((~![B_228: $i] : (tptp_fun__LE_(f(B_228), s(|'0'|)) | (~tptp_fun__LE_(f(B_228), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_228)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.19/0.51 tff(302,plain,
% 0.19/0.51 (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[301, 166])).
% 0.19/0.51 tff(303,plain,
% 0.19/0.51 (tptp_fun__E_(s(|'0'|), f(z))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[302, 296, 298])).
% 0.19/0.51 tff(304,plain,
% 0.19/0.51 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(305,plain,
% 0.19/0.51 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(306,plain,
% 0.19/0.51 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.19/0.51 tff(307,plain,
% 0.19/0.51 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[306, 234])).
% 0.19/0.51 tff(308,plain,
% 0.19/0.51 (iLEQ(suc(z), suc(z))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[307, 303, 297])).
% 0.19/0.51 tff(309,plain,
% 0.19/0.51 (((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(310,plain,
% 0.19/0.51 (((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(311,plain,
% 0.19/0.51 (((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[310])).
% 0.19/0.51 tff(312,plain,
% 0.19/0.51 (((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[311, 309])).
% 0.19/0.51 tff(313,plain,
% 0.19/0.51 ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | ((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(314,plain,
% 0.19/0.52 ((~![B_231: $i, B_229: $i, B_232: $i, B_230: $i, B_233: $i, A_2: $i] : ((~iLEQ(suc(B_231), suc(B_232))) | (~tptp_fun__E_(s(|'0'|), f(A_2))) | (~iLEQ(suc(B_232), suc(B_233))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_230)))) | (~tptp_fun__E_(s(|'0'|), f(B_230))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_231)))) | (~iLEQ(suc(B_229), suc(B_230))) | (~iLEQ(suc(A_2), suc(B_229))) | (~tptp_fun__E_(s(|'0'|), f(B_231))) | (~tptp_fun__E_(s(|'0'|), f(B_233))) | (~tptp_fun__E_(s(|'0'|), f(B_232))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_229)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_2)))) | (~tptp_fun__E_(s(|'0'|), f(B_229))) | (~iLEQ(suc(B_230), suc(B_231))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_232)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_233)))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.19/0.52 tff(315,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[314, 252, 297, 303, 308])).
% 0.19/0.52 tff(316,plain,(tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(317,plain,
% 0.19/0.52 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[316, 294, 119])).
% 0.19/0.52 tff(318,plain,
% 0.19/0.52 (tptp_fun__E_(|'0'|, f(z))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[155, 317])).
% 0.19/0.52 tff(319,plain,
% 0.19/0.52 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[203, 318])).
% 0.19/0.52 tff(320,plain,
% 0.19/0.52 (iLEQ(suc(z), suc(z))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[319, 268])).
% 0.19/0.52 tff(321,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[220, 214, 268, 318, 320])).
% 0.19/0.52 % SZS output end Proof
% 0.19/0.52 % E exiting
%------------------------------------------------------------------------------