%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO689-1 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:42:07 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO689-1 : TPTP v9.0.0. Released v7.3.0.
% 0.07/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Fri Jun 20 13:22:20 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% 0.20/0.39 tff(iLEQ_type, type, (
% 0.20/0.39 iLEQ: ( $i * $i ) > $o)).
% 0.20/0.39 tff(suc_type, type, (
% 0.20/0.39 suc: $i > $i)).
% 0.20/0.39 tff(z_type, type, (
% 0.20/0.39 z: $i)).
% 0.20/0.39 tff(tptp_fun__LE__type, type, (
% 0.20/0.39 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.20/0.39 tff(s_type, type, (
% 0.20/0.39 s: $i > $i)).
% 0.20/0.39 tff(tptp_fun__0__type, type, (
% 0.20/0.39 tptp_fun__0_: $i)).
% 0.20/0.39 tff(f_type, type, (
% 0.20/0.39 f: $i > $i)).
% 0.20/0.39 tff(tptp_fun__E__type, type, (
% 0.20/0.39 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.20/0.39 tff(1,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.20/0.39 tff(2,assumption,(~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))), introduced(assumption)).
% 0.20/0.39 tff(3,plain,
% 0.20/0.39 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))) <=> tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(4,plain,
% 0.20/0.39 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.39 tff(5,plain,
% 0.20/0.39 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|)))))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(6,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_583')).
% 0.20/0.39 tff(7,plain,
% 0.20/0.39 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.39 tff(8,plain,(
% 0.20/0.39 ![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[7])).
% 0.20/0.39 tff(9,plain,
% 0.20/0.39 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.39 tff(10,plain,
% 0.20/0.39 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(11,plain,
% 0.20/0.39 ($false),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.20/0.39 tff(12,plain,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.39 tff(13,plain,
% 0.20/0.39 (^[B_585: $i] : refl((tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|)))))))) <=> (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(14,plain,
% 0.20/0.39 (![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|)))))))) <=> ![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.39 tff(15,plain,
% 0.20/0.39 (![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|)))))))) <=> ![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(16,plain,
% 0.20/0.39 (^[B_585: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585)))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|)))))) <=> (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|)))))))))),
% 0.20/0.39 inference(bind,[status(th)],[])).
% 0.20/0.39 tff(17,plain,
% 0.20/0.39 (![B_585: $i] : (((~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585)))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|)))))) <=> ![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.39 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.39 tff(18,axiom,(![B_585: $i] : (((~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585)))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2050')).
% 0.20/0.39 tff(19,plain,
% 0.20/0.39 (![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.39 tff(20,plain,
% 0.20/0.39 (![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.20/0.39 tff(21,plain,(
% 0.20/0.39 ![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.39 inference(skolemize,[status(sab)],[20])).
% 0.20/0.39 tff(22,plain,
% 0.20/0.39 (![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.20/0.39 tff(23,plain,
% 0.20/0.39 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(24,plain,
% 0.20/0.39 ((tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|)))))))) <=> (tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.39 inference(rewrite,[status(thm)],[])).
% 0.20/0.39 tff(25,plain,
% 0.20/0.39 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|)))))))))),
% 0.20/0.39 inference(monotonicity,[status(thm)],[24])).
% 0.20/0.39 tff(26,plain,
% 0.20/0.39 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.39 inference(transitivity,[status(thm)],[25, 23])).
% 0.20/0.39 tff(27,plain,
% 0.20/0.39 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.39 inference(quant_inst,[status(thm)],[])).
% 0.20/0.39 tff(28,plain,
% 0.20/0.39 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|)))))))),
% 0.20/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.39 tff(29,plain,
% 0.20/0.39 (tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|)))))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[28, 22])).
% 0.20/0.39 tff(30,plain,
% 0.20/0.39 (tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[29, 12])).
% 0.20/0.39 tff(31,plain,
% 0.20/0.39 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))),
% 0.20/0.39 inference(unit_resolution,[status(thm)],[30, 1])).
% 0.20/0.40 tff(32,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))), introduced(assumption)).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[33, 9, 32])).
% 0.20/0.40 tff(35,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (^[B_585: $i] : refl((tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|)))))) <=> (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|)))))) <=> ![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|)))))) <=> ![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (^[B_585: $i] : rewrite((((~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|)))))) <=> (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 (![B_585: $i] : (((~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|)))))) <=> ![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.40 tff(41,axiom,(![B_585: $i] : (((~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2115')).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.20/0.40 tff(44,plain,(
% 0.20/0.40 ![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[43])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[48, 45, 35])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[49, 1])).
% 0.20/0.40 tff(51,assumption,(tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))), introduced(assumption)).
% 0.20/0.40 tff(52,assumption,(tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))), introduced(assumption)).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(54,plain,
% 0.20/0.40 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.40 tff(55,plain,
% 0.20/0.40 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(56,plain,
% 0.20/0.40 (^[A_1: $i] : rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(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(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(57,plain,
% 0.20/0.40 (![A_1: $i] : (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(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(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.40 tff(58,axiom,(![A_1: $i] : (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1581')).
% 0.20/0.40 tff(59,plain,
% 0.20/0.40 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.40 tff(60,plain,
% 0.20/0.40 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.20/0.40 tff(61,plain,(
% 0.20/0.40 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[60])).
% 0.20/0.40 tff(62,plain,
% 0.20/0.40 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.20/0.40 tff(63,plain,
% 0.20/0.40 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(64,plain,
% 0.20/0.40 ((iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(65,plain,
% 0.20/0.40 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[64])).
% 0.20/0.40 tff(66,plain,
% 0.20/0.40 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[65, 63])).
% 0.20/0.40 tff(67,plain,
% 0.20/0.40 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(68,plain,
% 0.20/0.40 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.40 tff(69,plain,
% 0.20/0.40 ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[68, 62])).
% 0.20/0.40 tff(70,plain,
% 0.20/0.40 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[69, 52, 51])).
% 0.20/0.40 tff(71,plain,
% 0.20/0.40 (^[B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : refl(((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(72,plain,
% 0.20/0.40 (![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) <=> ![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.20/0.40 tff(73,plain,
% 0.20/0.40 (![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) <=> ![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (^[B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $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(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) <=> ((~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), (((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) <=> (((~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~iLEQ(suc(B_588), suc(B_589)))))), rewrite((((~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~iLEQ(suc(B_588), suc(B_589)))) <=> ((~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), (((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) <=> ((~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), ((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) <=> (((~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))))), rewrite((((~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) <=> ((~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), ((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) <=> ((~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), (((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) <=> (((~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))))), rewrite((((~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) <=> ((~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), (((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) <=> ((~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), ((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) <=> (((~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))))), rewrite((((~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), ((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), (((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) <=> (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~iLEQ(suc(B_587), suc(B_588)))))), rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~iLEQ(suc(B_587), suc(B_588)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), (((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), ((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) <=> (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))))), rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), ((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), (((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) <=> (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~iLEQ(suc(B_589), suc(B_590)))))), rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~iLEQ(suc(B_589), suc(B_590)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), (((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), ((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) <=> (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))))), rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), ((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), (((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), (((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), ((((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_586)))) <=> (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~iLEQ(suc(A_1), suc(B_586)))))), rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~iLEQ(suc(A_1), suc(B_586)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), ((((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_586)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), (((((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_586)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586))))) <=> (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586))))))), rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), (((((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_586)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), ((((((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_586)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))) <=> (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))))), rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), ((((((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_586)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), (((((((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_586)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589))))) <=> (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589))))))), rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), (((((((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_586)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))))), ((((((((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_586)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587)))) <=> (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587)))))), rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))), ((((((((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_586)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : (((((((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_586)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587)))) <=> ![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[74])).
% 0.20/0.43 tff(76,axiom,(![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : (((((((((((((((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588))))) | (~iLEQ(suc(B_586), suc(B_587)))) | (~iLEQ(suc(B_588), suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590)))) | (~iLEQ(suc(B_587), suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586)))) | (~iLEQ(suc(B_589), suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_586)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1514')).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.20/0.43 tff(79,plain,(
% 0.20/0.43 ![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[78])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(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))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(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))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[82])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(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))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[83, 81])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(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))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(86,plain,
% 0.20/0.44 ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[86, 80, 52, 51, 70])).
% 0.20/0.44 tff(88,plain,((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[88, 50, 31])).
% 0.20/0.44 tff(90,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(91,assumption,(~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.20/0.44 tff(92,plain,
% 0.20/0.44 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.45 tff(95,plain,
% 0.20/0.45 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[94, 45, 12])).
% 0.20/0.45 tff(96,plain,
% 0.20/0.45 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[95, 91])).
% 0.20/0.45 tff(97,assumption,(~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))), introduced(assumption)).
% 0.20/0.45 tff(98,plain,
% 0.20/0.45 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(99,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[98, 9, 97])).
% 0.20/0.45 tff(100,plain,(tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(101,plain,
% 0.20/0.45 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(102,plain,
% 0.20/0.45 ((tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|)))))))) <=> (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(103,plain,
% 0.20/0.45 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|)))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.45 tff(104,plain,
% 0.20/0.45 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.45 tff(105,plain,
% 0.20/0.45 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(106,plain,
% 0.20/0.45 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|)))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.45 tff(107,plain,
% 0.20/0.45 (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|)))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[106, 22])).
% 0.20/0.45 tff(108,plain,
% 0.20/0.45 (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[107, 100])).
% 0.20/0.45 tff(109,plain,
% 0.20/0.45 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[108, 91])).
% 0.20/0.45 tff(110,assumption,(tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))), introduced(assumption)).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(112,plain,
% 0.20/0.45 ((iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[112])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[113, 111])).
% 0.20/0.45 tff(115,plain,
% 0.20/0.45 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[116, 62, 51])).
% 0.20/0.45 tff(118,plain,
% 0.20/0.45 (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[117, 110])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))))))),
% 0.20/0.45 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[121, 119])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(124,plain,
% 0.20/0.45 ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[124, 80, 51, 110, 118])).
% 0.20/0.46 tff(126,plain,((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[126, 109, 96])).
% 0.20/0.46 tff(128,plain,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(129,assumption,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.20/0.46 tff(130,assumption,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.20/0.46 tff(131,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.20/0.46 tff(132,assumption,(~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))), introduced(assumption)).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 (^[B_906: $i] : refl((tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906))) <=> (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(134,plain,
% 0.20/0.46 (![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906))) <=> ![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 (![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906))) <=> ![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (^[B_906: $i] : rewrite((((~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906))) | tptp_fun__LE_(f(B_906), s(s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 (![B_906: $i] : (((~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906))) | tptp_fun__LE_(f(B_906), s(s(s(|'0'|))))) <=> ![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.46 tff(138,axiom,(![B_906: $i] : (((~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906))) | tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1230')).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 (![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.20/0.46 tff(141,plain,(
% 0.20/0.46 ![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[140])).
% 0.20/0.46 tff(142,plain,
% 0.20/0.46 (![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.20/0.46 tff(143,plain,
% 0.20/0.46 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(144,plain,
% 0.20/0.46 ((tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(145,plain,
% 0.20/0.46 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[144])).
% 0.20/0.46 tff(146,plain,
% 0.20/0.46 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[145, 143])).
% 0.20/0.46 tff(147,plain,
% 0.20/0.46 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(148,plain,
% 0.20/0.46 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.46 tff(149,plain,
% 0.20/0.46 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[148, 142])).
% 0.20/0.46 tff(150,plain,
% 0.20/0.46 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[149, 131, 129])).
% 0.20/0.46 tff(151,plain,
% 0.20/0.46 (^[B_906: $i] : refl((tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|))))))) <=> (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(152,plain,
% 0.20/0.46 (![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|))))))) <=> ![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[151])).
% 0.20/0.46 tff(153,plain,
% 0.20/0.46 (![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|))))))) <=> ![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 (^[B_906: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906)))) | tptp_fun__LE_(f(B_906), s(s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 (![B_906: $i] : (((~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906)))) | tptp_fun__LE_(f(B_906), s(s(s(|'0'|))))) <=> ![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[154])).
% 0.20/0.46 tff(156,axiom,(![B_906: $i] : (((~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906)))) | tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1935')).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 (![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.20/0.46 tff(158,plain,
% 0.20/0.46 (![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.20/0.46 tff(159,plain,(
% 0.20/0.46 ![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[158])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 (![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[159, 152])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[163, 160])).
% 0.20/0.46 tff(165,plain,
% 0.20/0.46 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[164, 131, 130])).
% 0.20/0.46 tff(166,plain,
% 0.20/0.46 (^[A_2: $i] : refl((iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(167,plain,
% 0.20/0.46 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.46 tff(168,plain,
% 0.20/0.46 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(169,plain,
% 0.20/0.46 (^[A_2: $i] : rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(170,plain,
% 0.20/0.46 (![A_2: $i] : (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~tptp_fun__E_(s(s(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(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[169])).
% 0.20/0.46 tff(171,axiom,(![A_2: $i] : (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2227')).
% 0.20/0.46 tff(172,plain,
% 0.20/0.46 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.20/0.46 tff(173,plain,
% 0.20/0.46 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.20/0.46 tff(174,plain,(
% 0.20/0.46 ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[173])).
% 0.20/0.46 tff(175,plain,
% 0.20/0.46 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.20/0.46 tff(176,plain,
% 0.20/0.46 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(177,plain,
% 0.20/0.46 ((iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(178,plain,
% 0.20/0.46 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[177])).
% 0.20/0.46 tff(179,plain,
% 0.20/0.46 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[178, 176])).
% 0.20/0.46 tff(180,plain,
% 0.20/0.46 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(181,plain,
% 0.20/0.46 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.20/0.46 tff(182,plain,
% 0.20/0.46 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[181, 175])).
% 0.20/0.46 tff(183,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[182, 165, 150, 132])).
% 0.20/0.46 tff(184,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(185,plain,
% 0.20/0.46 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[184, 131, 130, 129])).
% 0.20/0.46 tff(186,plain,
% 0.20/0.46 (^[B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : refl(((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(187,plain,
% 0.20/0.46 (![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) <=> ![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[186])).
% 0.20/0.46 tff(188,plain,
% 0.20/0.46 (![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) <=> ![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(189,plain,
% 0.20/0.46 (^[B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $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(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), (((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), (((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), ((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~iLEQ(suc(B_909), suc(B_910)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~iLEQ(suc(B_909), suc(B_910)))) <=> ((~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), ((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) <=> ((~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), (((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) <=> (((~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))))), rewrite((((~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), (((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), ((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), ((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), (((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), (((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), ((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~iLEQ(suc(A_2), suc(B_907)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~iLEQ(suc(A_2), suc(B_907)))) <=> ((~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), ((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) <=> ((~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), (((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) <=> (((~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))))), rewrite((((~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) <=> ((~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), (((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) <=> ((~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), ((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) <=> (((~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))))), rewrite((((~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), ((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), (((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), (((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), ((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), ((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), (((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907))))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907))))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), (((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), ((((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907))))) | (~iLEQ(suc(B_910), suc(B_911)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~iLEQ(suc(B_910), suc(B_911)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~iLEQ(suc(B_910), suc(B_911)))) <=> ((~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), ((((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907))))) | (~iLEQ(suc(B_910), suc(B_911)))) <=> ((~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), (((((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907))))) | (~iLEQ(suc(B_910), suc(B_911)))) | (~iLEQ(suc(B_907), suc(B_908)))) <=> (((~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~iLEQ(suc(B_907), suc(B_908)))))), rewrite((((~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~iLEQ(suc(B_907), suc(B_908)))) <=> ((~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), (((((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907))))) | (~iLEQ(suc(B_910), suc(B_911)))) | (~iLEQ(suc(B_907), suc(B_908)))) <=> ((~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))))), ((((((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907))))) | (~iLEQ(suc(B_910), suc(B_911)))) | (~iLEQ(suc(B_907), suc(B_908)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909))))) <=> (((~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909))))))), rewrite((((~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))), ((((((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907))))) | (~iLEQ(suc(B_910), suc(B_911)))) | (~iLEQ(suc(B_907), suc(B_908)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(190,plain,
% 0.20/0.48 (![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : (((((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907))))) | (~iLEQ(suc(B_910), suc(B_911)))) | (~iLEQ(suc(B_907), suc(B_908)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909))))) <=> ![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[189])).
% 0.20/0.48 tff(191,axiom,(![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : (((((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910)))) | (~iLEQ(suc(B_909), suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908)))) | (~iLEQ(suc(A_2), suc(B_907)))) | (~iLEQ(suc(B_908), suc(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907))))) | (~iLEQ(suc(B_910), suc(B_911)))) | (~iLEQ(suc(B_907), suc(B_908)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_657')).
% 0.20/0.48 tff(192,plain,
% 0.20/0.48 (![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 (![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.20/0.48 tff(194,plain,(
% 0.20/0.48 ![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[193])).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 (![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 (((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 (((~tptp_fun__E_(s(s(s(|'0'|))), f(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(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(198,plain,
% 0.20/0.48 (((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(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(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))) <=> ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[197])).
% 0.20/0.48 tff(199,plain,
% 0.20/0.48 (((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(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(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))) <=> ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[198, 196])).
% 0.20/0.49 tff(200,plain,
% 0.20/0.49 ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(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(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(201,plain,
% 0.20/0.49 ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.20/0.49 tff(202,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[201, 195, 165, 150, 185])).
% 0.20/0.49 tff(203,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(204,plain,
% 0.20/0.49 (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[203, 128, 90])).
% 0.20/0.49 tff(205,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.20/0.49 tff(206,plain,
% 0.20/0.49 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(207,plain,
% 0.20/0.49 ((tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|)))))))) <=> (tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(208,plain,
% 0.20/0.49 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|)))))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[207])).
% 0.20/0.49 tff(209,plain,
% 0.20/0.49 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[208, 206])).
% 0.20/0.49 tff(210,plain,
% 0.20/0.49 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(211,plain,
% 0.20/0.49 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(s(|'0'|)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.20/0.49 tff(212,plain,
% 0.20/0.49 (tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[211, 22, 35])).
% 0.20/0.49 tff(213,plain,
% 0.20/0.49 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[212, 205])).
% 0.20/0.49 tff(214,plain,
% 0.20/0.49 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(s(|'0'|))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(215,plain,
% 0.20/0.49 (tptp_fun__LE_(f(suc(z)), s(s(s(s(s(|'0'|))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[214, 9])).
% 0.20/0.49 tff(216,plain,
% 0.20/0.49 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(217,plain,
% 0.20/0.49 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[218, 45])).
% 0.20/0.49 tff(220,plain,
% 0.20/0.49 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[219, 205, 215])).
% 0.20/0.49 tff(221,assumption,(tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))), introduced(assumption)).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(223,plain,
% 0.20/0.49 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(224,plain,
% 0.20/0.49 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[223])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[224, 222])).
% 0.20/0.49 tff(226,plain,
% 0.20/0.49 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[227, 62, 221])).
% 0.20/0.49 tff(229,plain,
% 0.20/0.49 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[228, 52])).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(232,plain,
% 0.20/0.49 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[231])).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[232, 230])).
% 0.20/0.50 tff(234,plain,
% 0.20/0.50 ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(235,plain,
% 0.20/0.50 ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.20/0.50 tff(236,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[235, 80, 221, 52, 229])).
% 0.20/0.50 tff(237,plain,((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(238,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[237, 220, 213])).
% 0.20/0.50 tff(239,plain,(tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(240,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))), introduced(assumption)).
% 0.20/0.50 tff(241,plain,
% 0.20/0.50 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(242,plain,
% 0.20/0.50 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(243,plain,
% 0.20/0.50 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.20/0.50 tff(244,plain,
% 0.20/0.50 (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[243, 160])).
% 0.20/0.50 tff(245,plain,
% 0.20/0.50 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[244, 240, 129])).
% 0.20/0.50 tff(246,assumption,(tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.20/0.50 tff(247,plain,
% 0.20/0.50 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(248,plain,
% 0.20/0.50 ((tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(249,plain,
% 0.20/0.50 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[248])).
% 0.20/0.50 tff(250,plain,
% 0.20/0.50 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[249, 247])).
% 0.20/0.50 tff(251,plain,
% 0.20/0.50 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(252,plain,
% 0.20/0.50 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.50 tff(253,plain,
% 0.20/0.50 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[252, 142])).
% 0.20/0.50 tff(254,plain,
% 0.20/0.50 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[253, 240, 246])).
% 0.20/0.50 tff(255,plain,
% 0.20/0.50 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(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(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(256,plain,
% 0.20/0.50 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(257,plain,
% 0.20/0.50 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[256])).
% 0.20/0.50 tff(258,plain,
% 0.20/0.50 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[257, 255])).
% 0.20/0.50 tff(259,plain,
% 0.20/0.50 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(260,plain,
% 0.20/0.50 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.20/0.50 tff(261,plain,
% 0.20/0.50 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[260, 175])).
% 0.20/0.50 tff(262,plain,
% 0.20/0.50 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[261, 254, 245])).
% 0.20/0.50 tff(263,plain,
% 0.20/0.50 (((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(264,plain,
% 0.20/0.50 (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(265,plain,
% 0.20/0.50 (((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))))) <=> ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[264])).
% 0.20/0.50 tff(266,plain,
% 0.20/0.50 (((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))))) <=> ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[265, 263])).
% 0.20/0.50 tff(267,plain,
% 0.20/0.50 ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(268,plain,
% 0.20/0.51 ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.20/0.51 tff(269,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[268, 195, 254, 245, 262])).
% 0.20/0.51 tff(270,plain,(tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(271,plain,
% 0.20/0.51 (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[270, 90, 239])).
% 0.20/0.51 tff(272,assumption,(~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.20/0.51 tff(273,plain,
% 0.20/0.51 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(274,plain,
% 0.20/0.51 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(275,plain,
% 0.20/0.51 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(s(|'0'|)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.20/0.51 tff(276,plain,
% 0.20/0.51 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(s(|'0'|)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[275, 22])).
% 0.20/0.51 tff(277,plain,
% 0.20/0.51 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[276, 272, 215])).
% 0.20/0.51 tff(278,plain,
% 0.20/0.51 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(279,plain,
% 0.20/0.51 (tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[278, 9])).
% 0.20/0.51 tff(280,plain,
% 0.20/0.51 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(281,plain,
% 0.20/0.51 ((tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) <=> (tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(282,plain,
% 0.20/0.51 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[281])).
% 0.20/0.51 tff(283,plain,
% 0.20/0.51 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[282, 280])).
% 0.20/0.51 tff(284,plain,
% 0.20/0.51 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(285,plain,
% 0.20/0.51 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[284, 283])).
% 0.20/0.51 tff(286,plain,
% 0.20/0.51 (tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(s(s(|'0'|)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[285, 45])).
% 0.20/0.51 tff(287,plain,
% 0.20/0.51 (tptp_fun__LE_(f(z), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[286, 279])).
% 0.20/0.51 tff(288,plain,
% 0.20/0.51 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[287, 272])).
% 0.20/0.51 tff(289,assumption,(tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))), introduced(assumption)).
% 0.20/0.51 tff(290,plain,
% 0.20/0.51 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(291,plain,
% 0.20/0.51 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(292,plain,
% 0.20/0.51 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.20/0.51 tff(293,plain,
% 0.20/0.51 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[292, 62])).
% 0.20/0.51 tff(294,plain,
% 0.20/0.51 (iLEQ(suc(z), suc(z))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[293, 289, 221])).
% 0.20/0.51 tff(295,plain,
% 0.20/0.51 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(296,plain,
% 0.20/0.51 (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z)))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(297,plain,
% 0.20/0.51 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[296])).
% 0.20/0.51 tff(298,plain,
% 0.20/0.51 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[297, 295])).
% 0.20/0.51 tff(299,plain,
% 0.20/0.51 ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(300,plain,
% 0.20/0.51 ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.20/0.51 tff(301,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[300, 80, 221, 289, 294])).
% 0.20/0.51 tff(302,plain,((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(z))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(303,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[302, 288, 277])).
% 0.20/0.51 tff(304,plain,(tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(305,assumption,(~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.20/0.52 tff(306,plain,
% 0.20/0.52 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(307,plain,
% 0.20/0.52 ((tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(308,plain,
% 0.20/0.52 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[307])).
% 0.20/0.52 tff(309,plain,
% 0.20/0.52 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[308, 306])).
% 0.20/0.52 tff(310,plain,
% 0.20/0.52 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(311,plain,
% 0.20/0.52 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.20/0.52 tff(312,plain,
% 0.20/0.52 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[311, 142])).
% 0.20/0.52 tff(313,plain,
% 0.20/0.52 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[312, 305, 128])).
% 0.20/0.52 tff(314,assumption,(~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.20/0.52 tff(315,plain,
% 0.20/0.52 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(316,plain,
% 0.20/0.52 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(317,plain,
% 0.20/0.52 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_585)) | (~tptp_fun__LE_(f(B_585), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.20/0.52 tff(318,plain,
% 0.20/0.52 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[317, 45, 100])).
% 0.20/0.52 tff(319,plain,
% 0.20/0.52 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[318, 314])).
% 0.20/0.52 tff(320,assumption,(~tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|))))))), introduced(assumption)).
% 0.20/0.52 tff(321,plain,
% 0.20/0.52 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(322,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[321, 9, 320])).
% 0.20/0.52 tff(323,plain,(tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(324,plain,
% 0.20/0.52 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(325,plain,
% 0.20/0.52 ((tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|)))))))) <=> (tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(326,plain,
% 0.20/0.52 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|)))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[325])).
% 0.20/0.52 tff(327,plain,
% 0.20/0.52 (((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[326, 324])).
% 0.20/0.52 tff(328,plain,
% 0.20/0.52 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(329,plain,
% 0.20/0.52 ((~![B_585: $i] : (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_585))) | tptp_fun__LE_(f(B_585), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(B_585)), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|)))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.20/0.52 tff(330,plain,
% 0.20/0.52 (tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(suc(z)))))), s(s(s(s(s(|'0'|)))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[329, 22])).
% 0.20/0.52 tff(331,plain,
% 0.20/0.52 (tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[330, 323])).
% 0.20/0.52 tff(332,plain,
% 0.20/0.52 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[331, 314])).
% 0.20/0.52 tff(333,assumption,(tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))), introduced(assumption)).
% 0.20/0.52 tff(334,plain,
% 0.20/0.52 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(335,plain,
% 0.20/0.52 ((iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(336,plain,
% 0.20/0.52 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))))))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[335])).
% 0.38/0.53 tff(337,plain,
% 0.38/0.53 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))))),
% 0.38/0.53 inference(transitivity,[status(thm)],[336, 334])).
% 0.38/0.53 tff(338,plain,
% 0.38/0.53 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))))),
% 0.38/0.53 inference(quant_inst,[status(thm)],[])).
% 0.38/0.53 tff(339,plain,
% 0.38/0.53 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))))),
% 0.38/0.53 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.38/0.53 tff(340,plain,
% 0.38/0.53 (iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z))))))))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[339, 62, 110])).
% 0.38/0.53 tff(341,plain,
% 0.38/0.53 (iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))),
% 0.38/0.53 inference(unit_resolution,[status(thm)],[340, 333])).
% 0.38/0.53 tff(342,plain,
% 0.38/0.53 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(343,plain,
% 0.38/0.53 (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))))),
% 0.38/0.53 inference(rewrite,[status(thm)],[])).
% 0.38/0.53 tff(344,plain,
% 0.38/0.53 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))))))),
% 0.38/0.53 inference(monotonicity,[status(thm)],[343])).
% 0.38/0.53 tff(345,plain,
% 0.38/0.53 (((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))))) <=> ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))))),
% 0.38/0.53 inference(transitivity,[status(thm)],[344, 342])).
% 0.38/0.53 tff(346,plain,
% 0.38/0.53 ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(347,plain,
% 0.38/0.54 ((~![B_589: $i, B_587: $i, B_588: $i, B_586: $i, A_1: $i, B_590: $i] : ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_590)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_590))) | (~iLEQ(suc(B_588), suc(B_589))) | (~iLEQ(suc(B_586), suc(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_587))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_589)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_1))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_586)))) | (~iLEQ(suc(A_1), suc(B_586))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(A_1)))) | (~iLEQ(suc(B_589), suc(B_590))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_586))) | (~iLEQ(suc(B_587), suc(B_588))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_589))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_587)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(B_588)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_588))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~iLEQ(suc(suc(suc(suc(suc(z))))), suc(suc(suc(suc(suc(z)))))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.38/0.54 tff(348,plain,
% 0.38/0.54 ($false),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[347, 80, 110, 333, 341])).
% 0.38/0.54 tff(349,plain,((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(suc(z)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(suc(suc(suc(suc(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.54 tff(350,plain,
% 0.38/0.54 ($false),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[349, 332, 319])).
% 0.38/0.54 tff(351,plain,(tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.54 tff(352,plain,
% 0.38/0.54 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(353,plain,
% 0.38/0.54 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(354,plain,
% 0.38/0.54 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.38/0.54 tff(355,plain,
% 0.38/0.54 (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[354, 160])).
% 0.38/0.54 tff(356,plain,
% 0.38/0.54 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[355, 305, 351])).
% 0.38/0.54 tff(357,assumption,(tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))), introduced(assumption)).
% 0.38/0.54 tff(358,assumption,(tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))), introduced(assumption)).
% 0.38/0.54 tff(359,plain,
% 0.38/0.54 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(360,plain,
% 0.38/0.54 ((iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(361,plain,
% 0.38/0.54 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[360])).
% 0.38/0.54 tff(362,plain,
% 0.38/0.54 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))))),
% 0.38/0.54 inference(transitivity,[status(thm)],[361, 359])).
% 0.38/0.54 tff(363,plain,
% 0.38/0.54 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(364,plain,
% 0.38/0.54 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.38/0.54 tff(365,plain,
% 0.38/0.54 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[364, 175])).
% 0.38/0.54 tff(366,plain,
% 0.38/0.54 (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[365, 358, 357])).
% 0.38/0.54 tff(367,plain,
% 0.38/0.54 (((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))) <=> ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(368,plain,
% 0.38/0.54 (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(369,plain,
% 0.38/0.54 (((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))) <=> ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))))))),
% 0.38/0.54 inference(monotonicity,[status(thm)],[368])).
% 0.38/0.54 tff(370,plain,
% 0.38/0.54 (((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))) <=> ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))),
% 0.38/0.54 inference(transitivity,[status(thm)],[369, 367])).
% 0.38/0.54 tff(371,plain,
% 0.38/0.54 ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(372,plain,
% 0.38/0.54 ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.38/0.55 tff(373,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[372, 195, 357, 358, 366])).
% 0.38/0.55 tff(374,plain,((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.55 tff(375,plain,
% 0.38/0.55 ($false),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[374, 356, 313])).
% 0.38/0.55 tff(376,plain,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.55 tff(377,assumption,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.38/0.55 tff(378,assumption,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.38/0.55 tff(379,assumption,(tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.38/0.55 tff(380,assumption,(tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))), introduced(assumption)).
% 0.38/0.55 tff(381,assumption,(~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 0.38/0.55 tff(382,assumption,(~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))), introduced(assumption)).
% 0.38/0.55 tff(383,plain,
% 0.38/0.55 (^[B_1066: $i] : refl((tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|)))))) <=> (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|)))))))),
% 0.38/0.55 inference(bind,[status(th)],[])).
% 0.38/0.55 tff(384,plain,
% 0.38/0.55 (![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|)))))) <=> ![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))),
% 0.38/0.55 inference(quant_intro,[status(thm)],[383])).
% 0.38/0.55 tff(385,plain,
% 0.38/0.55 (![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|)))))) <=> ![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(386,plain,
% 0.38/0.55 (^[B_1066: $i] : rewrite((((~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|)))) <=> (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|)))))))),
% 0.38/0.55 inference(bind,[status(th)],[])).
% 0.38/0.55 tff(387,plain,
% 0.38/0.55 (![B_1066: $i] : (((~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|)))) <=> ![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))),
% 0.38/0.55 inference(quant_intro,[status(thm)],[386])).
% 0.38/0.55 tff(388,axiom,(![B_1066: $i] : (((~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1314')).
% 0.38/0.55 tff(389,plain,
% 0.38/0.55 (![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.38/0.55 tff(390,plain,
% 0.38/0.55 (![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[389, 385])).
% 0.38/0.55 tff(391,plain,(
% 0.38/0.55 ![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))),
% 0.38/0.55 inference(skolemize,[status(sab)],[390])).
% 0.38/0.55 tff(392,plain,
% 0.38/0.55 (![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[391, 384])).
% 0.39/0.55 tff(393,plain,
% 0.39/0.55 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), 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_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), 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'|))))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(394,plain,
% 0.39/0.55 ((tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(z))), 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'|))))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(395,plain,
% 0.39/0.55 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))) <=> ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), 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'|)))))))),
% 0.39/0.55 inference(monotonicity,[status(thm)],[394])).
% 0.39/0.55 tff(396,plain,
% 0.39/0.55 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))) <=> ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), 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'|))))))),
% 0.39/0.55 inference(transitivity,[status(thm)],[395, 393])).
% 0.39/0.55 tff(397,plain,
% 0.39/0.55 ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(398,plain,
% 0.39/0.55 ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), 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'|)))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[397, 396])).
% 0.39/0.55 tff(399,plain,
% 0.39/0.55 (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'|)))))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[398, 392])).
% 0.39/0.55 tff(400,plain,
% 0.39/0.55 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[399, 382, 377])).
% 0.39/0.55 tff(401,plain,
% 0.39/0.55 (^[B_1136: $i] : refl((tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|))))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(402,plain,
% 0.39/0.55 (![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|))))) <=> ![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[401])).
% 0.39/0.55 tff(403,plain,
% 0.39/0.55 (![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|))))) <=> ![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(404,plain,
% 0.39/0.55 (^[B_1136: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_1136)))) | tptp_fun__LE_(f(B_1136), s(|'0'|))) <=> (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|))))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(405,plain,
% 0.39/0.55 (![B_1136: $i] : (((~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_1136)))) | tptp_fun__LE_(f(B_1136), s(|'0'|))) <=> ![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[404])).
% 0.39/0.55 tff(406,axiom,(![B_1136: $i] : (((~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_1136)))) | tptp_fun__LE_(f(B_1136), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1440')).
% 0.39/0.55 tff(407,plain,
% 0.39/0.55 (![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[406, 405])).
% 0.39/0.55 tff(408,plain,
% 0.39/0.55 (![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[407, 403])).
% 0.39/0.55 tff(409,plain,(
% 0.39/0.55 ![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))),
% 0.39/0.55 inference(skolemize,[status(sab)],[408])).
% 0.39/0.55 tff(410,plain,
% 0.39/0.55 (![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[409, 402])).
% 0.39/0.55 tff(411,plain,
% 0.39/0.55 (((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))) <=> ((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(412,plain,
% 0.39/0.55 ((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(413,plain,
% 0.39/0.55 ((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.39/0.55 tff(414,plain,
% 0.39/0.55 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[413, 410])).
% 0.39/0.55 tff(415,plain,
% 0.39/0.55 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[414, 400, 381])).
% 0.39/0.55 tff(416,plain,
% 0.39/0.55 (^[B_1161: $i] : refl((tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|)))) <=> (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|)))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(417,plain,
% 0.39/0.55 (![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|)))) <=> ![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[416])).
% 0.39/0.55 tff(418,plain,
% 0.39/0.55 (![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|)))) <=> ![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(419,plain,
% 0.39/0.55 (^[B_1161: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_1161)))) | tptp_fun__LE_(f(B_1161), |'0'|)) <=> (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|)))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(420,plain,
% 0.39/0.55 (![B_1161: $i] : (((~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_1161)))) | tptp_fun__LE_(f(B_1161), |'0'|)) <=> ![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[419])).
% 0.39/0.55 tff(421,axiom,(![B_1161: $i] : (((~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_1161)))) | tptp_fun__LE_(f(B_1161), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_113')).
% 0.39/0.55 tff(422,plain,
% 0.39/0.55 (![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.39/0.55 tff(423,plain,
% 0.39/0.55 (![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[422, 418])).
% 0.39/0.55 tff(424,plain,(
% 0.39/0.55 ![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))))),
% 0.39/0.55 inference(skolemize,[status(sab)],[423])).
% 0.39/0.55 tff(425,plain,
% 0.39/0.55 (![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[424, 417])).
% 0.39/0.55 tff(426,plain,
% 0.39/0.55 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(427,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1092')).
% 0.39/0.55 tff(428,plain,
% 0.39/0.55 (~tptp_fun__LE_(f(z), |'0'|)),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.39/0.55 tff(429,plain,
% 0.39/0.55 (((~![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))) <=> ((~![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(430,plain,
% 0.39/0.55 ((~![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(431,plain,
% 0.39/0.55 ((~![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_1161))) | (~tptp_fun__LE_(f(suc(B_1161)), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.39/0.55 tff(432,plain,
% 0.39/0.55 (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[431, 428, 425])).
% 0.39/0.55 tff(433,plain,
% 0.39/0.55 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[432, 415])).
% 0.39/0.55 tff(434,assumption,(tptp_fun__E_(|'0'|, f(suc(z)))), introduced(assumption)).
% 0.39/0.55 tff(435,assumption,(tptp_fun__E_(|'0'|, f(z))), introduced(assumption)).
% 0.39/0.55 tff(436,plain,
% 0.39/0.55 (^[A_5: $i] : refl((iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) <=> (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(437,plain,
% 0.39/0.55 (![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) <=> ![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[436])).
% 0.39/0.55 tff(438,plain,
% 0.39/0.55 (![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) <=> ![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(439,plain,
% 0.39/0.55 (^[A_5: $i] : rewrite((((~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | iLEQ(suc(A_5), suc(A_5))) <=> (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(440,plain,
% 0.39/0.55 (![A_5: $i] : (((~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | iLEQ(suc(A_5), suc(A_5))) <=> ![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[439])).
% 0.39/0.55 tff(441,axiom,(![A_5: $i] : (((~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | iLEQ(suc(A_5), suc(A_5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2293')).
% 0.39/0.55 tff(442,plain,
% 0.39/0.55 (![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.39/0.55 tff(443,plain,
% 0.39/0.55 (![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[442, 438])).
% 0.39/0.55 tff(444,plain,(
% 0.39/0.55 ![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))))),
% 0.39/0.55 inference(skolemize,[status(sab)],[443])).
% 0.39/0.55 tff(445,plain,
% 0.39/0.55 (![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[444, 437])).
% 0.39/0.55 tff(446,plain,
% 0.39/0.55 (((~![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(447,plain,
% 0.39/0.55 ((~![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.39/0.55 inference(quant_inst,[status(thm)],[])).
% 0.39/0.55 tff(448,plain,
% 0.39/0.55 ((~![A_5: $i] : (iLEQ(suc(A_5), suc(A_5)) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.39/0.55 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.39/0.55 tff(449,plain,
% 0.39/0.55 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[448, 445])).
% 0.39/0.55 tff(450,plain,
% 0.39/0.55 (iLEQ(suc(z), suc(z))),
% 0.39/0.55 inference(unit_resolution,[status(thm)],[449, 435, 434])).
% 0.39/0.55 tff(451,plain,
% 0.39/0.55 (^[B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : refl(((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))),
% 0.39/0.55 inference(bind,[status(th)],[])).
% 0.39/0.55 tff(452,plain,
% 0.39/0.55 (![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) <=> ![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))),
% 0.39/0.55 inference(quant_intro,[status(thm)],[451])).
% 0.39/0.55 tff(453,plain,
% 0.39/0.55 (![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) <=> ![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))),
% 0.39/0.55 inference(rewrite,[status(thm)],[])).
% 0.39/0.55 tff(454,plain,
% 0.39/0.55 (^[B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $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_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), (((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~iLEQ(suc(A_5), suc(B_1162)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~iLEQ(suc(A_5), suc(B_1162)))) <=> ((~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), (((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) <=> ((~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), ((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) <=> (((~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(A_5)))))), rewrite((((~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) <=> ((~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), ((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) <=> ((~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), (((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) <=> (((~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), (((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), ((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) <=> (((~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), ((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), (((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) <=> (((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), (((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), ((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) <=> (((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), ((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), (((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) <=> (((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(B_1166)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), (((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), ((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) <=> (((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~iLEQ(suc(B_1165), suc(B_1166)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), ((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), (((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) <=> (((~tptp_fun__E_(|'0'|, f(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), (((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) <=> (((~tptp_fun__E_(|'0'|, f(B_1164))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_1164))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164))))) <=> (((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164))))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164))))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), ((((((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162))))) <=> (((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162))))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), ((((((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162))))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), (((((((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162))))) | (~iLEQ(suc(B_1164), suc(B_1165)))) <=> (((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~iLEQ(suc(B_1164), suc(B_1165)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~iLEQ(suc(B_1164), suc(B_1165)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), (((((((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162))))) | (~iLEQ(suc(B_1164), suc(B_1165)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))))), ((((((((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162))))) | (~iLEQ(suc(B_1164), suc(B_1165)))) | (~tptp_fun__E_(|'0'|, f(B_1163)))) <=> (((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(B_1163)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165)))) | (~tptp_fun__E_(|'0'|, f(B_1163)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))), ((((((((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162))))) | (~iLEQ(suc(B_1164), suc(B_1165)))) | (~tptp_fun__E_(|'0'|, f(B_1163)))) <=> ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))))),
% 0.39/0.56 inference(bind,[status(th)],[])).
% 0.39/0.56 tff(455,plain,
% 0.39/0.56 (![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : (((((((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162))))) | (~iLEQ(suc(B_1164), suc(B_1165)))) | (~tptp_fun__E_(|'0'|, f(B_1163)))) <=> ![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))),
% 0.39/0.56 inference(quant_intro,[status(thm)],[454])).
% 0.39/0.56 tff(456,axiom,(![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : (((((((((((((((((~tptp_fun__E_(|'0'|, f(B_1165))) | (~iLEQ(suc(B_1162), suc(B_1163)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163))))) | (~iLEQ(suc(A_5), suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162)))) | (~tptp_fun__E_(|'0'|, f(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166))))) | (~tptp_fun__E_(|'0'|, f(B_1166)))) | (~iLEQ(suc(B_1165), suc(B_1166)))) | (~iLEQ(suc(B_1163), suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164))))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162))))) | (~iLEQ(suc(B_1164), suc(B_1165)))) | (~tptp_fun__E_(|'0'|, f(B_1163))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_421')).
% 0.39/0.56 tff(457,plain,
% 0.39/0.56 (![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.39/0.57 tff(458,plain,
% 0.39/0.57 (![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[457, 453])).
% 0.39/0.57 tff(459,plain,(
% 0.39/0.57 ![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))),
% 0.39/0.57 inference(skolemize,[status(sab)],[458])).
% 0.39/0.57 tff(460,plain,
% 0.39/0.57 (![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[459, 452])).
% 0.39/0.57 tff(461,plain,
% 0.39/0.57 (((~![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(462,plain,
% 0.39/0.57 (((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(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(suc(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)))) | (~iLEQ(suc(z), suc(z))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(463,plain,
% 0.39/0.57 (((~![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(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(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))))) <=> ((~![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))))),
% 0.39/0.57 inference(monotonicity,[status(thm)],[462])).
% 0.39/0.57 tff(464,plain,
% 0.39/0.57 (((~![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(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(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))))) <=> ((~![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.39/0.57 inference(transitivity,[status(thm)],[463, 461])).
% 0.39/0.57 tff(465,plain,
% 0.39/0.57 ((~![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(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(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 0.39/0.57 inference(quant_inst,[status(thm)],[])).
% 0.39/0.57 tff(466,plain,
% 0.39/0.57 ((~![B_1165: $i, B_1163: $i, B_1166: $i, A_5: $i, B_1162: $i, B_1164: $i] : ((~tptp_fun__E_(|'0'|, f(B_1164))) | (~tptp_fun__E_(|'0'|, f(suc(B_1164)))) | (~tptp_fun__E_(|'0'|, f(B_1163))) | (~iLEQ(suc(B_1164), suc(B_1165))) | (~tptp_fun__E_(|'0'|, f(suc(B_1162)))) | (~tptp_fun__E_(|'0'|, f(suc(B_1165)))) | (~iLEQ(suc(B_1163), suc(B_1164))) | (~iLEQ(suc(B_1165), suc(B_1166))) | (~tptp_fun__E_(|'0'|, f(B_1166))) | (~tptp_fun__E_(|'0'|, f(suc(B_1166)))) | (~tptp_fun__E_(|'0'|, f(suc(A_5)))) | (~tptp_fun__E_(|'0'|, f(B_1162))) | (~tptp_fun__E_(|'0'|, f(A_5))) | (~iLEQ(suc(A_5), suc(B_1162))) | (~tptp_fun__E_(|'0'|, f(suc(B_1163)))) | (~iLEQ(suc(B_1162), suc(B_1163))) | (~tptp_fun__E_(|'0'|, f(B_1165))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.39/0.57 tff(467,plain,
% 0.39/0.57 ($false),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[466, 460, 434, 435, 450])).
% 0.39/0.57 tff(468,plain,((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.57 tff(469,plain,
% 0.39/0.57 (~tptp_fun__E_(|'0'|, f(z))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[468, 433])).
% 0.39/0.57 tff(470,plain,
% 0.39/0.57 (^[B_1161: $i] : refl((tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161))) <=> (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(471,plain,
% 0.39/0.57 (![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161))) <=> ![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161)))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[470])).
% 0.39/0.57 tff(472,plain,
% 0.39/0.57 (![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161))) <=> ![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161)))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(473,plain,
% 0.39/0.57 (^[B_1161: $i] : rewrite((((~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161))) | tptp_fun__LE_(f(B_1161), |'0'|)) <=> (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(474,plain,
% 0.39/0.57 (![B_1161: $i] : (((~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161))) | tptp_fun__LE_(f(B_1161), |'0'|)) <=> ![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161)))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[473])).
% 0.39/0.57 tff(475,axiom,(![B_1161: $i] : (((~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161))) | tptp_fun__LE_(f(B_1161), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_328')).
% 0.39/0.57 tff(476,plain,
% 0.39/0.57 (![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.39/0.57 tff(477,plain,
% 0.39/0.57 (![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[476, 472])).
% 0.39/0.57 tff(478,plain,(
% 0.39/0.57 ![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161)))),
% 0.39/0.57 inference(skolemize,[status(sab)],[477])).
% 0.39/0.57 tff(479,plain,
% 0.39/0.57 (![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161)))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[478, 471])).
% 0.39/0.57 tff(480,plain,
% 0.39/0.57 (((~![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(481,plain,
% 0.39/0.57 ((~![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.39/0.57 inference(quant_inst,[status(thm)],[])).
% 0.39/0.57 tff(482,plain,
% 0.39/0.57 ((~![B_1161: $i] : (tptp_fun__LE_(f(B_1161), |'0'|) | (~tptp_fun__LE_(f(B_1161), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_1161)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[481, 480])).
% 0.39/0.57 tff(483,plain,
% 0.39/0.57 ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[482, 479, 428])).
% 0.39/0.57 tff(484,plain,
% 0.39/0.57 (~tptp_fun__LE_(f(z), s(|'0'|))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[483, 469])).
% 0.39/0.57 tff(485,plain,
% 0.39/0.57 (^[B_1066: $i] : refl((tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|)))))) <=> (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|)))))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(486,plain,
% 0.39/0.57 (![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|)))))) <=> ![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[485])).
% 0.39/0.57 tff(487,plain,
% 0.39/0.57 (![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|)))))) <=> ![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(488,plain,
% 0.39/0.57 (^[B_1066: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066)))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|)))) <=> (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|)))))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(489,plain,
% 0.39/0.57 (![B_1066: $i] : (((~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066)))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|)))) <=> ![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[488])).
% 0.39/0.57 tff(490,axiom,(![B_1066: $i] : (((~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066)))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_388')).
% 0.39/0.57 tff(491,plain,
% 0.39/0.57 (![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.39/0.57 tff(492,plain,
% 0.39/0.57 (![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[491, 487])).
% 0.39/0.57 tff(493,plain,(
% 0.39/0.57 ![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))),
% 0.39/0.57 inference(skolemize,[status(sab)],[492])).
% 0.39/0.57 tff(494,plain,
% 0.39/0.57 (![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[493, 486])).
% 0.39/0.57 tff(495,plain,
% 0.39/0.57 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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'|))))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(496,plain,
% 0.39/0.57 ((tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(z))), 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'|))))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(497,plain,
% 0.39/0.57 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))) <=> ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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'|)))))))),
% 0.39/0.57 inference(monotonicity,[status(thm)],[496])).
% 0.39/0.57 tff(498,plain,
% 0.39/0.57 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))) <=> ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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'|))))))),
% 0.39/0.57 inference(transitivity,[status(thm)],[497, 495])).
% 0.39/0.57 tff(499,plain,
% 0.39/0.57 ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.39/0.57 inference(quant_inst,[status(thm)],[])).
% 0.39/0.57 tff(500,plain,
% 0.39/0.57 ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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'|)))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.39/0.57 tff(501,plain,
% 0.39/0.57 (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'|)))))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[500, 494])).
% 0.39/0.57 tff(502,plain,
% 0.39/0.57 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[501, 382, 377])).
% 0.39/0.57 tff(503,plain,
% 0.39/0.57 (((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 0.39/0.57 inference(rewrite,[status(thm)],[])).
% 0.39/0.57 tff(504,plain,
% 0.39/0.57 ((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 0.39/0.57 inference(quant_inst,[status(thm)],[])).
% 0.39/0.57 tff(505,plain,
% 0.39/0.57 ((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_1136))) | (~tptp_fun__LE_(f(suc(B_1136)), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 0.39/0.57 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.39/0.57 tff(506,plain,
% 0.39/0.57 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[505, 410])).
% 0.39/0.57 tff(507,plain,
% 0.39/0.57 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.39/0.57 inference(unit_resolution,[status(thm)],[506, 484, 502])).
% 0.39/0.57 tff(508,assumption,(~iLEQ(suc(z), suc(z))), introduced(assumption)).
% 0.39/0.57 tff(509,assumption,(~tptp_fun__LE_(f(z), s(|'0'|))), introduced(assumption)).
% 0.39/0.57 tff(510,assumption,(tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 0.39/0.57 tff(511,plain,
% 0.39/0.57 (^[A_4: $i] : refl((iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) <=> (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))))),
% 0.39/0.57 inference(bind,[status(th)],[])).
% 0.39/0.57 tff(512,plain,
% 0.39/0.57 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) <=> ![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))),
% 0.39/0.57 inference(quant_intro,[status(thm)],[511])).
% 0.39/0.58 tff(513,plain,
% 0.39/0.58 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) <=> ![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(514,plain,
% 0.39/0.58 (^[A_4: $i] : rewrite((((~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | iLEQ(suc(A_4), suc(A_4))) <=> (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(515,plain,
% 0.39/0.58 (![A_4: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | iLEQ(suc(A_4), suc(A_4))) <=> ![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[514])).
% 0.39/0.58 tff(516,axiom,(![A_4: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | iLEQ(suc(A_4), suc(A_4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1329')).
% 0.39/0.58 tff(517,plain,
% 0.39/0.58 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[516, 515])).
% 0.39/0.58 tff(518,plain,
% 0.39/0.58 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[517, 513])).
% 0.39/0.58 tff(519,plain,(
% 0.39/0.58 ![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))),
% 0.39/0.58 inference(skolemize,[status(sab)],[518])).
% 0.39/0.58 tff(520,plain,
% 0.39/0.58 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[519, 512])).
% 0.39/0.58 tff(521,plain,
% 0.39/0.58 (((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(522,plain,
% 0.39/0.58 ((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(523,plain,
% 0.39/0.58 ((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.39/0.58 tff(524,plain,
% 0.39/0.58 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[523, 520])).
% 0.39/0.58 tff(525,plain,
% 0.39/0.58 (~tptp_fun__E_(s(|'0'|), f(z))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[524, 508, 510])).
% 0.39/0.58 tff(526,plain,
% 0.39/0.58 (^[B_1136: $i] : refl((tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136))) <=> (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(527,plain,
% 0.39/0.58 (![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136))) <=> ![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[526])).
% 0.39/0.58 tff(528,plain,
% 0.39/0.58 (![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136))) <=> ![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(529,plain,
% 0.39/0.58 (^[B_1136: $i] : rewrite((((~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136))) | tptp_fun__LE_(f(B_1136), s(|'0'|))) <=> (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(530,plain,
% 0.39/0.58 (![B_1136: $i] : (((~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136))) | tptp_fun__LE_(f(B_1136), s(|'0'|))) <=> ![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[529])).
% 0.39/0.58 tff(531,axiom,(![B_1136: $i] : (((~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136))) | tptp_fun__LE_(f(B_1136), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_740')).
% 0.39/0.58 tff(532,plain,
% 0.39/0.58 (![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.39/0.58 tff(533,plain,
% 0.39/0.58 (![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[532, 528])).
% 0.39/0.58 tff(534,plain,(
% 0.39/0.58 ![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))),
% 0.39/0.58 inference(skolemize,[status(sab)],[533])).
% 0.39/0.58 tff(535,plain,
% 0.39/0.58 (![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[534, 527])).
% 0.39/0.58 tff(536,plain,
% 0.39/0.58 (((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))) <=> ((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(537,plain,
% 0.39/0.58 ((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(538,plain,
% 0.39/0.58 ((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.39/0.58 tff(539,plain,
% 0.39/0.58 (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[538, 535])).
% 0.39/0.58 tff(540,plain,
% 0.39/0.58 (~tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[539, 525, 509])).
% 0.39/0.58 tff(541,plain,
% 0.39/0.58 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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'|))))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(542,plain,
% 0.39/0.58 ((tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(z)), 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'|))))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(543,plain,
% 0.39/0.58 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))) <=> ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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'|)))))))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[542])).
% 0.39/0.58 tff(544,plain,
% 0.39/0.58 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))) <=> ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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'|))))))),
% 0.39/0.58 inference(transitivity,[status(thm)],[543, 541])).
% 0.39/0.58 tff(545,plain,
% 0.39/0.58 ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(546,plain,
% 0.39/0.58 ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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'|)))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[545, 544])).
% 0.39/0.58 tff(547,plain,
% 0.39/0.58 (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'|)))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[546, 494])).
% 0.39/0.58 tff(548,plain,
% 0.39/0.58 (tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[547, 540, 380])).
% 0.39/0.58 tff(549,plain,
% 0.39/0.58 (^[A_3: $i] : refl((iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))) <=> (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(550,plain,
% 0.39/0.58 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))) <=> ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[549])).
% 0.39/0.58 tff(551,plain,
% 0.39/0.58 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))) <=> ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(552,plain,
% 0.39/0.58 (^[A_3: $i] : rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | iLEQ(suc(A_3), suc(A_3))) <=> (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(553,plain,
% 0.39/0.58 (![A_3: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'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_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[552])).
% 0.39/0.58 tff(554,axiom,(![A_3: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | iLEQ(suc(A_3), suc(A_3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1218')).
% 0.39/0.58 tff(555,plain,
% 0.39/0.58 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.39/0.58 tff(556,plain,
% 0.39/0.58 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[555, 551])).
% 0.39/0.58 tff(557,plain,(
% 0.39/0.58 ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))),
% 0.39/0.58 inference(skolemize,[status(sab)],[556])).
% 0.39/0.58 tff(558,plain,
% 0.39/0.58 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[557, 550])).
% 0.39/0.58 tff(559,plain,
% 0.39/0.58 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))) <=> ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(560,plain,
% 0.39/0.58 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(561,plain,
% 0.39/0.58 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.39/0.58 tff(562,plain,
% 0.39/0.58 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[561, 558])).
% 0.39/0.58 tff(563,plain,
% 0.39/0.58 (~tptp_fun__E_(s(s(|'0'|)), f(z))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[562, 548, 508])).
% 0.39/0.58 tff(564,plain,
% 0.39/0.58 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(z)) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))))) <=> ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(|'0'|)), f(z)) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(565,plain,
% 0.39/0.58 ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(z)) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(566,plain,
% 0.39/0.58 ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(|'0'|)), f(z)) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|)))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.39/0.58 tff(567,plain,
% 0.39/0.58 (tptp_fun__E_(s(s(|'0'|)), f(z)) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|)))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[566, 392])).
% 0.39/0.58 tff(568,plain,
% 0.39/0.58 (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[567, 563, 540])).
% 0.39/0.58 tff(569,plain,
% 0.39/0.58 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(570,plain,
% 0.39/0.58 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(571,plain,
% 0.39/0.58 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_906))) | (~tptp_fun__LE_(f(suc(B_906)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[570, 569])).
% 0.39/0.58 tff(572,plain,
% 0.39/0.58 (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[571, 160])).
% 0.39/0.58 tff(573,plain,
% 0.39/0.58 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[572, 568, 246])).
% 0.39/0.58 tff(574,plain,
% 0.39/0.58 (((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(z)))) <=> ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(z)))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(575,plain,
% 0.39/0.58 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(z)))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(576,plain,
% 0.39/0.58 ((~![B_906: $i] : (tptp_fun__LE_(f(B_906), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_906), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_906)))) | tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(z))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.39/0.58 tff(577,plain,
% 0.39/0.58 (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(z))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[576, 142])).
% 0.39/0.58 tff(578,plain,
% 0.39/0.58 (tptp_fun__E_(s(s(s(|'0'|))), f(z))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[577, 568, 379])).
% 0.39/0.58 tff(579,plain,
% 0.39/0.58 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(580,plain,
% 0.39/0.58 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(581,plain,
% 0.39/0.58 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[580, 579])).
% 0.39/0.58 tff(582,plain,
% 0.39/0.58 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z)))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[581, 175])).
% 0.39/0.58 tff(583,plain,
% 0.39/0.58 ($false),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[582, 578, 573, 508])).
% 0.39/0.58 tff(584,plain,(iLEQ(suc(z), suc(z)) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.58 tff(585,plain,
% 0.39/0.58 (iLEQ(suc(z), suc(z))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[584, 484, 246, 380, 379, 507])).
% 0.39/0.58 tff(586,plain,
% 0.39/0.58 (^[B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : refl(((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(587,plain,
% 0.39/0.58 (![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) <=> ![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[586])).
% 0.39/0.58 tff(588,plain,
% 0.39/0.58 (![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) <=> ![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(589,plain,
% 0.39/0.59 (^[B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $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(((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~iLEQ(suc(B_1138), suc(B_1139)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) <=> ((~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) <=> ((~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) <=> (((~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))))), rewrite((((~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~iLEQ(suc(B_1137), suc(B_1138)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) <=> ((~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) <=> ((~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) <=> (((~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~iLEQ(suc(A_4), suc(B_1137)))))), rewrite((((~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~iLEQ(suc(A_4), suc(B_1137)))) <=> ((~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) <=> ((~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) <=> (((~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~iLEQ(suc(B_1139), suc(B_1140)))))), rewrite((((~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~iLEQ(suc(B_1139), suc(B_1140)))) <=> ((~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) <=> ((~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) <=> (((~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))))), rewrite((((~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~iLEQ(suc(B_1140), suc(B_1141)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) <=> ((~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) <=> ((~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) <=> (((~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))))), rewrite((((~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), ((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141))))) | (~tptp_fun__E_(s(|'0'|), f(B_1139)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(B_1139)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(B_1139)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), ((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141))))) | (~tptp_fun__E_(s(|'0'|), f(B_1139)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141))))) | (~tptp_fun__E_(s(|'0'|), f(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(A_4)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(A_4)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(A_4)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141))))) | (~tptp_fun__E_(s(|'0'|), f(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(A_4)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))))), ((((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141))))) | (~tptp_fun__E_(s(|'0'|), f(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(A_4)))) | (~tptp_fun__E_(s(|'0'|), f(B_1138)))) <=> (((~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(B_1138)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137))))) | (~tptp_fun__E_(s(|'0'|), f(B_1138)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))), ((((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141))))) | (~tptp_fun__E_(s(|'0'|), f(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(A_4)))) | (~tptp_fun__E_(s(|'0'|), f(B_1138)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(590,plain,
% 0.39/0.60 (![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141))))) | (~tptp_fun__E_(s(|'0'|), f(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(A_4)))) | (~tptp_fun__E_(s(|'0'|), f(B_1138)))) <=> ![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[589])).
% 0.39/0.60 tff(591,axiom,(![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : (((((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139))))) | (~iLEQ(suc(B_1138), suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138))))) | (~iLEQ(suc(B_1137), suc(B_1138)))) | (~iLEQ(suc(A_4), suc(B_1137)))) | (~iLEQ(suc(B_1139), suc(B_1140)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140))))) | (~iLEQ(suc(B_1140), suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141))))) | (~tptp_fun__E_(s(|'0'|), f(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(A_4)))) | (~tptp_fun__E_(s(|'0'|), f(B_1138))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_327')).
% 0.39/0.60 tff(592,plain,
% 0.39/0.60 (![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.39/0.60 tff(593,plain,
% 0.39/0.60 (![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[592, 588])).
% 0.39/0.60 tff(594,plain,(
% 0.39/0.60 ![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))),
% 0.39/0.60 inference(skolemize,[status(sab)],[593])).
% 0.39/0.60 tff(595,plain,
% 0.39/0.60 (![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[594, 587])).
% 0.39/0.60 tff(596,plain,
% 0.39/0.60 (((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(597,plain,
% 0.39/0.60 (((~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)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(598,plain,
% 0.39/0.60 (((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | ((~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)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~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)))))) <=> ((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z)))))),
% 0.39/0.60 inference(monotonicity,[status(thm)],[597])).
% 0.39/0.60 tff(599,plain,
% 0.39/0.60 (((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | ((~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)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~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)))))) <=> ((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.39/0.60 inference(transitivity,[status(thm)],[598, 596])).
% 0.39/0.60 tff(600,plain,
% 0.39/0.60 ((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | ((~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)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~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)))))),
% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
% 0.39/0.60 tff(601,plain,
% 0.39/0.60 ((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[600, 599])).
% 0.39/0.60 tff(602,plain,
% 0.39/0.60 (~tptp_fun__E_(s(|'0'|), f(z))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[601, 595, 507, 585])).
% 0.39/0.60 tff(603,plain,
% 0.39/0.60 (~tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[539, 602, 484])).
% 0.39/0.60 tff(604,plain,
% 0.39/0.60 (tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[547, 603, 380])).
% 0.39/0.60 tff(605,plain,
% 0.39/0.60 (^[B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : refl(((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(606,plain,
% 0.39/0.60 (![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) <=> ![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[605])).
% 0.39/0.60 tff(607,plain,
% 0.39/0.60 (![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) <=> ![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(608,plain,
% 0.39/0.61 (^[B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $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(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), (((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), (((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), ((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), ((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), (((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~iLEQ(suc(B_1067), suc(B_1068)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), (((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), ((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), ((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), (((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), (((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), ((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~iLEQ(suc(B_1068), suc(B_1069)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~iLEQ(suc(B_1068), suc(B_1069)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), ((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), (((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), (((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), ((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~iLEQ(suc(A_3), suc(B_1067)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~iLEQ(suc(A_3), suc(B_1067)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), ((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), (((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), (((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~iLEQ(suc(B_1069), suc(B_1070)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), (((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), (((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), ((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), ((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), (((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), (((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))))), ((((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))) | (~iLEQ(suc(B_1070), suc(B_1071)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~iLEQ(suc(B_1070), suc(B_1071)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~iLEQ(suc(B_1070), suc(B_1071)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))), ((((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))) | (~iLEQ(suc(B_1070), suc(B_1071)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(609,plain,
% 0.39/0.62 (![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : (((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))) | (~iLEQ(suc(B_1070), suc(B_1071)))) <=> ![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[608])).
% 0.39/0.62 tff(610,axiom,(![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : (((((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068))))) | (~iLEQ(suc(B_1067), suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067)))) | (~iLEQ(suc(B_1068), suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071)))) | (~iLEQ(suc(A_3), suc(B_1067)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069))))) | (~iLEQ(suc(B_1069), suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3)))) | (~iLEQ(suc(B_1070), suc(B_1071))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_1712')).
% 0.39/0.62 tff(611,plain,
% 0.39/0.62 (![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.39/0.62 tff(612,plain,
% 0.39/0.62 (![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[611, 607])).
% 0.39/0.62 tff(613,plain,(
% 0.39/0.62 ![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))),
% 0.47/0.62 inference(skolemize,[status(sab)],[612])).
% 0.47/0.62 tff(614,plain,
% 0.47/0.62 (![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))),
% 0.47/0.62 inference(modus_ponens,[status(thm)],[613, 606])).
% 0.47/0.62 tff(615,plain,
% 0.47/0.62 (((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.47/0.62 inference(rewrite,[status(thm)],[])).
% 0.47/0.62 tff(616,plain,
% 0.47/0.62 (((~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))) | (~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)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), 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(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))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.47/0.62 inference(rewrite,[status(thm)],[])).
% 0.47/0.62 tff(617,plain,
% 0.47/0.62 (((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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))) | (~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)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), 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(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)))))) <=> ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.47/0.62 inference(monotonicity,[status(thm)],[616])).
% 0.47/0.62 tff(618,plain,
% 0.47/0.62 (((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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))) | (~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)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), 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(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)))))) <=> ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[617, 615])).
% 0.47/0.63 tff(619,plain,
% 0.47/0.63 ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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))) | (~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)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), 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(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)))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(620,plain,
% 0.47/0.63 ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.47/0.63 tff(621,plain,
% 0.47/0.63 ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[620, 614, 585])).
% 0.47/0.63 tff(622,plain,
% 0.47/0.63 (~tptp_fun__E_(s(s(|'0'|)), f(z))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[621, 604])).
% 0.47/0.63 tff(623,plain,
% 0.47/0.63 (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[567, 622, 603])).
% 0.47/0.63 tff(624,plain,
% 0.47/0.63 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[572, 623, 246])).
% 0.47/0.63 tff(625,plain,
% 0.47/0.63 (tptp_fun__E_(s(s(s(|'0'|))), f(z))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[577, 623, 379])).
% 0.47/0.63 tff(626,plain,
% 0.47/0.63 (((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(627,plain,
% 0.47/0.63 (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(628,plain,
% 0.47/0.63 (((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))))) <=> ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[627])).
% 0.47/0.63 tff(629,plain,
% 0.47/0.63 (((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))))) <=> ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[628, 626])).
% 0.47/0.63 tff(630,plain,
% 0.47/0.63 ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(631,plain,
% 0.47/0.63 ((~![B_911: $i, B_907: $i, B_910: $i, A_2: $i, B_908: $i, B_909: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_909)))) | (~iLEQ(suc(B_907), suc(B_908))) | (~iLEQ(suc(B_910), suc(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_907)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_911)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_909))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_908)))) | (~iLEQ(suc(B_908), suc(B_909))) | (~iLEQ(suc(A_2), suc(B_907))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_908))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_910)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_2))) | (~iLEQ(suc(B_909), suc(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_910))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_911))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_2)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_907))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[630, 629])).
% 0.47/0.63 tff(632,plain,
% 0.47/0.63 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z)))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[631, 195, 585])).
% 0.47/0.63 tff(633,plain,
% 0.47/0.63 ($false),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[632, 625, 624])).
% 0.47/0.63 tff(634,plain,(tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.63 tff(635,plain,
% 0.47/0.63 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[634, 381, 246, 380, 379, 377])).
% 0.47/0.63 tff(636,plain,
% 0.47/0.63 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | ((~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_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (~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)))))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(637,plain,
% 0.47/0.63 ((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)))))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(638,plain,
% 0.47/0.63 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (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_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | ((~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))))))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[637])).
% 0.47/0.63 tff(639,plain,
% 0.47/0.63 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (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_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (~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)))))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[638, 636])).
% 0.47/0.63 tff(640,plain,
% 0.47/0.63 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (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))))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(641,plain,
% 0.47/0.63 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (~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))))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[640, 639])).
% 0.47/0.63 tff(642,plain,
% 0.47/0.63 ((~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))))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[641, 558])).
% 0.47/0.63 tff(643,plain,
% 0.47/0.63 (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[642, 635, 132])).
% 0.47/0.63 tff(644,plain,
% 0.47/0.63 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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'|))))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(645,plain,
% 0.47/0.63 ((tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), 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'|))))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(646,plain,
% 0.47/0.63 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))))) <=> ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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'|)))))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[645])).
% 0.47/0.63 tff(647,plain,
% 0.47/0.63 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))))) <=> ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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'|))))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[646, 644])).
% 0.47/0.63 tff(648,plain,
% 0.47/0.63 ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(649,plain,
% 0.47/0.63 ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(suc(B_1066))) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(B_1066)), 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'|)))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[648, 647])).
% 0.47/0.63 tff(650,plain,
% 0.47/0.63 (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'|)))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[649, 494])).
% 0.47/0.64 tff(651,plain,
% 0.47/0.64 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[650, 643, 378])).
% 0.47/0.64 tff(652,plain,
% 0.47/0.64 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[414, 651, 381])).
% 0.47/0.64 tff(653,plain,
% 0.47/0.64 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[432, 652])).
% 0.47/0.64 tff(654,plain,
% 0.47/0.64 (~tptp_fun__E_(|'0'|, f(z))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[468, 653])).
% 0.47/0.64 tff(655,plain,
% 0.47/0.64 (~tptp_fun__LE_(f(z), s(|'0'|))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[483, 654])).
% 0.47/0.64 tff(656,assumption,(tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))), introduced(assumption)).
% 0.47/0.64 tff(657,assumption,(tptp_fun__E_(s(s(|'0'|)), f(suc(z)))), introduced(assumption)).
% 0.47/0.64 tff(658,plain,
% 0.47/0.64 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | ((~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_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (~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))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(659,plain,
% 0.47/0.64 ((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))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(660,plain,
% 0.47/0.64 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (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_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | ((~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)))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[659])).
% 0.47/0.64 tff(661,plain,
% 0.47/0.64 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (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_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (~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))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[660, 658])).
% 0.47/0.64 tff(662,plain,
% 0.47/0.64 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (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)))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(663,plain,
% 0.47/0.64 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))))) | (~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)))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.47/0.64 tff(664,plain,
% 0.47/0.64 ((~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)))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[663, 558])).
% 0.47/0.64 tff(665,plain,
% 0.47/0.64 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[664, 657, 656])).
% 0.47/0.64 tff(666,plain,
% 0.47/0.64 (((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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))))))) <=> ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | (~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))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(667,plain,
% 0.47/0.64 (((~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)))) | (~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))))) | (~iLEQ(suc(suc(z)), 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(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(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)))))) <=> ((~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))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(668,plain,
% 0.47/0.64 (((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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)))) | (~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))))) | (~iLEQ(suc(suc(z)), 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(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(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))))))) <=> ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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)))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[667])).
% 0.47/0.64 tff(669,plain,
% 0.47/0.64 (((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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)))) | (~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))))) | (~iLEQ(suc(suc(z)), 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(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(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))))))) <=> ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | (~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))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[668, 666])).
% 0.47/0.64 tff(670,plain,
% 0.47/0.64 ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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)))) | (~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))))) | (~iLEQ(suc(suc(z)), 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(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(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))))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(671,plain,
% 0.47/0.64 ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.47/0.64 tff(672,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[671, 614, 657, 656, 665])).
% 0.47/0.64 tff(673,plain,((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(674,plain,
% 0.47/0.64 (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[673, 635])).
% 0.47/0.64 tff(675,plain,
% 0.47/0.64 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), 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_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), 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'|))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(676,plain,
% 0.47/0.64 ((tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(z)), 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'|))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(677,plain,
% 0.47/0.64 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))) <=> ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), 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'|)))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[676])).
% 0.47/0.64 tff(678,plain,
% 0.47/0.64 (((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))) <=> ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), 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'|))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[677, 675])).
% 0.47/0.64 tff(679,plain,
% 0.47/0.64 ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(680,plain,
% 0.47/0.64 ((~![B_1066: $i] : (tptp_fun__E_(s(s(|'0'|)), f(B_1066)) | tptp_fun__LE_(f(B_1066), s(s(|'0'|))) | (~tptp_fun__LE_(f(B_1066), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[679, 678])).
% 0.47/0.64 tff(681,plain,
% 0.47/0.64 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[680, 392])).
% 0.47/0.64 tff(682,plain,
% 0.47/0.64 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[681, 674, 380])).
% 0.47/0.64 tff(683,plain,
% 0.47/0.64 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[506, 682, 655])).
% 0.47/0.64 tff(684,plain,
% 0.47/0.64 (iLEQ(suc(z), suc(z))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[584, 683, 246, 380, 379, 655])).
% 0.47/0.64 tff(685,plain,
% 0.47/0.64 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[547, 674, 380])).
% 0.47/0.64 tff(686,plain,
% 0.47/0.64 (tptp_fun__E_(s(|'0'|), f(z))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[539, 685, 655])).
% 0.47/0.64 tff(687,plain,
% 0.47/0.64 ($false),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[601, 595, 683, 686, 684])).
% 0.47/0.64 tff(688,plain,(tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.64 tff(689,plain,
% 0.47/0.64 (tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[688, 380, 246, 379, 378, 132, 377])).
% 0.47/0.64 tff(690,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 0.47/0.64 tff(691,plain,
% 0.47/0.64 (((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(692,plain,
% 0.47/0.64 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(693,plain,
% 0.47/0.64 (((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))) | (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_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[692])).
% 0.47/0.64 tff(694,plain,
% 0.47/0.64 (((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))) | (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_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[693, 691])).
% 0.47/0.64 tff(695,plain,
% 0.47/0.64 ((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(696,plain,
% 0.47/0.64 ((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[695, 694])).
% 0.47/0.64 tff(697,plain,
% 0.47/0.64 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[696, 520])).
% 0.47/0.64 tff(698,plain,
% 0.47/0.64 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[697, 510, 690])).
% 0.47/0.64 tff(699,plain,
% 0.47/0.64 (((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(700,plain,
% 0.47/0.64 (((~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))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(701,plain,
% 0.47/0.65 (((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | ((~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))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[700])).
% 0.47/0.65 tff(702,plain,
% 0.47/0.65 (((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | ((~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))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[701, 699])).
% 0.47/0.65 tff(703,plain,
% 0.47/0.65 ((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | ((~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))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(704,plain,
% 0.47/0.65 ((~![B_1140: $i, B_1139: $i, A_4: $i, B_1137: $i, B_1141: $i, B_1138: $i] : ((~tptp_fun__E_(s(|'0'|), f(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(A_4))) | (~tptp_fun__E_(s(|'0'|), f(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1141)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_4)))) | (~iLEQ(suc(B_1140), suc(B_1141))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1140)))) | (~iLEQ(suc(B_1139), suc(B_1140))) | (~iLEQ(suc(A_4), suc(B_1137))) | (~iLEQ(suc(B_1137), suc(B_1138))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1138)))) | (~tptp_fun__E_(s(|'0'|), f(B_1137))) | (~tptp_fun__E_(s(|'0'|), f(B_1141))) | (~iLEQ(suc(B_1138), suc(B_1139))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1139)))) | (~tptp_fun__E_(s(|'0'|), f(B_1140))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_1137)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.47/0.65 tff(705,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[704, 595, 510, 690, 698])).
% 0.47/0.65 tff(706,plain,((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(707,plain,
% 0.47/0.65 (~tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[706, 689])).
% 0.47/0.65 tff(708,assumption,(~tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 0.47/0.65 tff(709,assumption,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 0.47/0.65 tff(710,plain,
% 0.47/0.65 (((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(711,plain,
% 0.47/0.65 ((tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))) <=> (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(712,plain,
% 0.47/0.65 (((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))) | (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_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[711])).
% 0.47/0.65 tff(713,plain,
% 0.47/0.65 (((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))) | (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_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[712, 710])).
% 0.47/0.65 tff(714,plain,
% 0.47/0.65 ((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))) | (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))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(715,plain,
% 0.47/0.65 ((~![B_1136: $i] : (tptp_fun__LE_(f(B_1136), s(|'0'|)) | (~tptp_fun__LE_(f(B_1136), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_1136)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[714, 713])).
% 0.47/0.65 tff(716,plain,
% 0.47/0.65 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[715, 535])).
% 0.47/0.65 tff(717,plain,
% 0.47/0.65 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[716, 709, 708])).
% 0.47/0.65 tff(718,plain,
% 0.47/0.65 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[432, 717])).
% 0.47/0.65 tff(719,plain,
% 0.47/0.65 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[506, 709, 708])).
% 0.47/0.65 tff(720,plain,
% 0.47/0.65 (tptp_fun__E_(|'0'|, f(z))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[483, 719])).
% 0.47/0.65 tff(721,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[468, 720, 718])).
% 0.47/0.65 tff(722,plain,((~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(723,plain,
% 0.47/0.65 (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[722, 707])).
% 0.47/0.65 tff(724,plain,
% 0.47/0.65 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[501, 723, 377])).
% 0.47/0.65 tff(725,plain,
% 0.47/0.65 (tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[681, 723, 380])).
% 0.47/0.65 tff(726,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[673, 725, 724])).
% 0.47/0.65 tff(727,plain,((~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(728,plain,
% 0.47/0.65 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[727, 376, 239, 304, 271, 204])).
% 0.47/0.65 tff(729,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 0.47/0.65 tff(730,plain,
% 0.47/0.65 (tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[681, 729, 380])).
% 0.47/0.65 tff(731,plain,
% 0.47/0.65 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[501, 729, 377])).
% 0.47/0.65 tff(732,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[673, 731, 730])).
% 0.47/0.65 tff(733,plain,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(734,plain,
% 0.47/0.65 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[733, 204, 271])).
% 0.47/0.65 tff(735,plain,
% 0.47/0.65 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[722, 734])).
% 0.47/0.65 tff(736,plain,
% 0.47/0.65 (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[706, 735])).
% 0.47/0.65 tff(737,plain,
% 0.47/0.65 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[634, 304, 239, 271, 736, 204])).
% 0.47/0.65 tff(738,plain,
% 0.47/0.65 (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[673, 737])).
% 0.47/0.65 tff(739,plain,
% 0.47/0.65 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[547, 738, 271])).
% 0.47/0.65 tff(740,plain,
% 0.47/0.65 (iLEQ(suc(z), suc(z))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[584, 509, 246, 380, 379, 510])).
% 0.47/0.65 tff(741,assumption,(tptp_fun__LE_(f(z), s(s(|'0'|)))), introduced(assumption)).
% 0.47/0.65 tff(742,plain,
% 0.47/0.65 (tptp_fun__E_(s(|'0'|), f(z))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[539, 509, 741])).
% 0.47/0.65 tff(743,plain,
% 0.47/0.65 ($false),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[601, 595, 510, 742, 740])).
% 0.47/0.65 tff(744,plain,(tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.47/0.65 tff(745,plain,
% 0.47/0.65 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[744, 739, 239, 271, 735, 304])).
% 0.47/0.65 tff(746,plain,
% 0.47/0.65 (tptp_fun__E_(|'0'|, f(z))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[483, 745])).
% 0.47/0.65 tff(747,plain,
% 0.47/0.65 (~tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[468, 746])).
% 0.47/0.65 tff(748,plain,
% 0.47/0.65 (~tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[432, 747])).
% 0.47/0.65 tff(749,plain,
% 0.47/0.65 (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[414, 748, 736])).
% 0.47/0.65 tff(750,plain,
% 0.47/0.65 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[650, 376, 749])).
% 0.47/0.65 tff(751,plain,
% 0.47/0.65 (((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | (~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))))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(752,plain,
% 0.47/0.65 (((~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))))) | (~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)))))) | (~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(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(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))))))) <=> ((~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))))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(753,plain,
% 0.47/0.65 (((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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))))) | (~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)))))) | (~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(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(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)))))))) <=> ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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)))))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[752])).
% 0.47/0.66 tff(754,plain,
% 0.47/0.66 (((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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))))) | (~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)))))) | (~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(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(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)))))))) <=> ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | (~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))))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[753, 751])).
% 0.47/0.66 tff(755,plain,
% 0.47/0.66 ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | ((~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))))) | (~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)))))) | (~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(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(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)))))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(756,plain,
% 0.47/0.66 ((~![B_1067: $i, B_1068: $i, B_1071: $i, B_1070: $i, A_3: $i, B_1069: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1069)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1069))) | (~iLEQ(suc(B_1068), suc(B_1069))) | (~iLEQ(suc(B_1070), suc(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_3))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1070)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1071)))) | (~iLEQ(suc(B_1069), suc(B_1070))) | (~iLEQ(suc(A_3), suc(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1071))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1067))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_3)))) | (~iLEQ(suc(B_1067), suc(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1068)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1068))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_1070))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_1067)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[755, 754])).
% 0.47/0.66 tff(757,plain,
% 0.47/0.66 ($false),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[756, 614, 737, 750, 728])).
% 0.47/0.66 % SZS output end Proof
% 0.47/0.66 % E exiting
%------------------------------------------------------------------------------