%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO683-1 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:42:06 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO683-1 : TPTP v9.0.0. Released v7.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 13:22:23 EDT 2025
% 0.18/0.33 % CPUTime :
% 0.18/0.39 % SZS status Unsatisfiable
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(tptp_fun__E__type, type, (
% 0.18/0.39 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.18/0.39 tff(f_type, type, (
% 0.18/0.39 f: $i > $i)).
% 0.18/0.39 tff(suc_type, type, (
% 0.18/0.39 suc: $i > $i)).
% 0.18/0.39 tff(z_type, type, (
% 0.18/0.39 z: $i)).
% 0.18/0.39 tff(s_type, type, (
% 0.18/0.39 s: $i > $i)).
% 0.18/0.39 tff(tptp_fun__0__type, type, (
% 0.18/0.39 tptp_fun__0_: $i)).
% 0.18/0.39 tff(tptp_fun__LE__type, type, (
% 0.18/0.39 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.18/0.39 tff(iLEQ_type, type, (
% 0.18/0.39 iLEQ: ( $i * $i ) > $o)).
% 0.18/0.39 tff(1,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 0.18/0.39 tff(2,assumption,(tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))), introduced(assumption)).
% 0.18/0.39 tff(3,assumption,(~iLEQ(suc(suc(z)), suc(suc(z)))), introduced(assumption)).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (^[A_2: $i] : refl((iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(5,plain,
% 0.18/0.39 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.18/0.39 tff(6,plain,
% 0.18/0.39 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(7,plain,
% 0.18/0.39 (^[A_2: $i] : rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(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(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(8,plain,
% 0.18/0.39 (![A_2: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(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(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[7])).
% 0.18/0.39 tff(9,axiom,(![A_2: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_29')).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.18/0.39 tff(11,plain,
% 0.18/0.39 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.18/0.39 tff(12,plain,(
% 0.18/0.39 ![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[11])).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | ((~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_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (~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))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 ((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))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (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_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | ((~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)))))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (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_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (~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))))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[16, 14])).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (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)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (~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)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 ((~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)))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[19, 13])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[20, 3, 2])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (^[B_247: $i] : refl(((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))) <=> ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))) <=> ![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))) <=> ![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (^[B_247: $i] : rewrite((((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))) | tptp_fun__LE_(f(B_247), s(s(|'0'|)))) <=> ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (![B_247: $i] : (((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))) | tptp_fun__LE_(f(B_247), s(s(|'0'|)))) <=> ![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.18/0.39 tff(27,axiom,(![B_247: $i] : (((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_247))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_97')).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 (![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.18/0.39 tff(30,plain,(
% 0.18/0.39 ![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[29])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | (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_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | 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'|))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (((~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(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~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))))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | (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'|)))))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[33])).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~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))))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | 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'|))))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[34, 32])).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~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))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | 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'|)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (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'|)))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[37, 31])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[38, 21, 1])).
% 0.18/0.39 tff(40,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(s(s(s(|'0'|))))) <=> tptp_fun__LE_(f(A), s(s(s(s(|'0'|))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|))))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|))))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(44,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_451')).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.18/0.40 tff(46,plain,(
% 0.18/0.40 ![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[45])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 ($false),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[48, 47, 40])).
% 0.18/0.40 tff(50,plain,(tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (^[B_158: $i] : refl((tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))) <=> (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[51])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 (^[B_158: $i] : rewrite((((~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))) | tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 (![B_158: $i] : (((~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))) | tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[54])).
% 0.18/0.40 tff(56,axiom,(![B_158: $i] : (((~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158))) | tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_539')).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.18/0.40 tff(59,plain,(
% 0.18/0.40 ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[58])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | ((~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 ((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__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (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_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | ((~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[62])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (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_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[63, 61])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (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))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[66, 60, 50])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[67, 39])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[69, 47])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (^[B_158: $i] : refl((tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))) <=> (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (^[B_158: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))) | tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (![B_158: $i] : (((~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))) | tptp_fun__LE_(f(B_158), s(s(s(|'0'|))))) <=> ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[74])).
% 0.18/0.40 tff(76,axiom,(![B_158: $i] : (((~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158)))) | tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_443')).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.40 tff(78,plain,
% 0.18/0.40 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.18/0.40 tff(79,plain,(
% 0.18/0.40 ![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[78])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 (![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(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_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(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)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(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)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(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))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.18/0.40 tff(84,plain,
% 0.18/0.40 (tptp_fun__LE_(f(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))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[83, 80])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[84, 39, 70])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(87,plain,
% 0.18/0.40 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.40 tff(88,plain,
% 0.18/0.40 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 (^[A_1: $i] : rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~tptp_fun__E_(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(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 (![A_1: $i] : (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~tptp_fun__E_(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(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[89])).
% 0.18/0.40 tff(91,axiom,(![A_1: $i] : (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_59')).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.18/0.40 tff(94,plain,(
% 0.18/0.40 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[93])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | ((~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(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~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(suc(z))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 ((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)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | ((~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(suc(z)))))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[97])).
% 0.18/0.41 tff(99,plain,
% 0.18/0.41 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~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(suc(z))))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[98, 96])).
% 0.18/0.41 tff(100,plain,
% 0.18/0.41 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (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)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(101,plain,
% 0.18/0.41 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.18/0.41 tff(102,plain,
% 0.18/0.41 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[101, 95])).
% 0.18/0.41 tff(103,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[102, 85, 68, 3])).
% 0.18/0.41 tff(104,plain,(iLEQ(suc(suc(z)), suc(suc(z))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[104, 2, 1])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 (^[B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : refl(((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(107,plain,
% 0.18/0.41 (![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) <=> ![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[106])).
% 0.18/0.41 tff(108,plain,
% 0.18/0.41 (![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) <=> ![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(109,plain,
% 0.18/0.41 (^[B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(A_2), suc(B_248)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(A_2), suc(B_248)))) <=> ((~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) <=> ((~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), (((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) <=> (((~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))))), rewrite((((~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), (((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), ((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), (((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(B_249), suc(B_250)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(B_249), suc(B_250)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), (((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), ((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), (((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), (((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), ((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), (((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), (((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), ((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(B_248), suc(B_249)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(B_248), suc(B_249)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), (((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), (((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))))), (((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) | (~iLEQ(suc(B_250), suc(B_251)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(B_250), suc(B_251)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249))))) | (~iLEQ(suc(B_250), suc(B_251)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))), (((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) | (~iLEQ(suc(B_250), suc(B_251)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(110,plain,
% 0.20/0.42 (![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) | (~iLEQ(suc(B_250), suc(B_251)))) <=> ![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.43 tff(111,axiom,(![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((((((((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250)))) | (~iLEQ(suc(A_2), suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251))))) | (~iLEQ(suc(B_249), suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250))))) | (~iLEQ(suc(B_248), suc(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) | (~iLEQ(suc(B_250), suc(B_251))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_563')).
% 0.20/0.43 tff(112,plain,
% 0.20/0.43 (![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.43 tff(113,plain,
% 0.20/0.43 (![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.20/0.43 tff(114,plain,(
% 0.20/0.43 ![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[113])).
% 0.20/0.43 tff(115,plain,
% 0.20/0.43 (![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.20/0.43 tff(116,plain,
% 0.20/0.43 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(117,plain,
% 0.20/0.43 (((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~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))))) | (~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))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(118,plain,
% 0.20/0.43 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~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(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))))) | (~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))))) | (~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))))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.43 tff(119,plain,
% 0.20/0.43 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~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(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))))) | (~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))))) | (~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))))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[118, 116])).
% 0.20/0.43 tff(120,plain,
% 0.20/0.43 ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~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(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))))) | (~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))))) | (~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))))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(121,plain,
% 0.20/0.43 ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.44 tff(122,plain,
% 0.20/0.44 (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[121, 115, 2, 105])).
% 0.20/0.44 tff(123,plain,
% 0.20/0.44 (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[38, 122, 1])).
% 0.20/0.44 tff(124,plain,
% 0.20/0.44 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[67, 123])).
% 0.20/0.44 tff(125,plain,
% 0.20/0.44 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[84, 123, 70])).
% 0.20/0.44 tff(126,plain,
% 0.20/0.44 (^[B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : refl(((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) <=> ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(127,plain,
% 0.20/0.44 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) <=> ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[126])).
% 0.20/0.44 tff(128,plain,
% 0.20/0.44 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) <=> ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(129,plain,
% 0.20/0.44 (^[B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(B_160), suc(B_161)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(B_160), suc(B_161)))) <=> ((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) <=> ((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), (((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) <=> (((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))))), rewrite((((~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), (((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), ((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), (((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), (((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), ((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), (((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(B_159), suc(B_160)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(B_159), suc(B_160)))) <=> ((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), (((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) <=> ((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), ((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> (((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))))), rewrite((((~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), (((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), (((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), ((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(B_161), suc(B_162)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(B_161), suc(B_162)))) <=> ((~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) <=> ((~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), (((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) <=> (((~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))))), rewrite((((~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), (((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), ((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), ((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))))), (((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(A_1), suc(B_159)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159))))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))), (((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(130,plain,
% 0.20/0.46 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_159)))) <=> ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.46 tff(131,axiom,(![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((((((((((((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162)))) | (~iLEQ(suc(B_160), suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160)))) | (~iLEQ(suc(B_159), suc(B_160)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161))))) | (~iLEQ(suc(B_161), suc(B_162)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_159))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_560')).
% 0.20/0.46 tff(132,plain,
% 0.20/0.46 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.46 tff(133,plain,
% 0.20/0.46 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.20/0.46 tff(134,plain,(
% 0.20/0.46 ![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[133])).
% 0.20/0.46 tff(135,plain,
% 0.20/0.46 (![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.20/0.46 tff(136,plain,
% 0.20/0.46 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~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)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(137,plain,
% 0.20/0.46 (((~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))))) | (~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)))) | (~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(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(138,plain,
% 0.20/0.46 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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))))) | (~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)))) | (~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(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[137])).
% 0.20/0.46 tff(139,plain,
% 0.20/0.46 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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))))) | (~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)))) | (~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(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~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)))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[138, 136])).
% 0.20/0.46 tff(140,plain,
% 0.20/0.46 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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))))) | (~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)))) | (~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(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(141,plain,
% 0.20/0.47 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.20/0.47 tff(142,plain,
% 0.20/0.47 ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[141, 135, 105])).
% 0.20/0.47 tff(143,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[142, 125, 124])).
% 0.20/0.47 tff(144,plain,((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(145,plain,
% 0.20/0.47 (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[144, 1])).
% 0.20/0.47 tff(146,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.20/0.47 tff(147,assumption,(~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.20/0.47 tff(148,plain,
% 0.20/0.47 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(149,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[148, 47, 147])).
% 0.20/0.47 tff(150,plain,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(151,plain,
% 0.20/0.47 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (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__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | 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__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(152,plain,
% 0.20/0.47 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (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__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(153,plain,
% 0.20/0.47 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.20/0.47 tff(154,plain,
% 0.20/0.47 (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[153, 80, 150])).
% 0.20/0.47 tff(155,plain,
% 0.20/0.47 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[154, 146])).
% 0.20/0.47 tff(156,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.20/0.47 tff(157,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[69, 47, 156])).
% 0.20/0.47 tff(158,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(159,plain,
% 0.20/0.47 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | ((~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__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (~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__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(160,plain,
% 0.20/0.47 ((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__LE_(f(suc(suc(z))), s(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(|'0'|)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(161,plain,
% 0.20/0.47 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (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_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | ((~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__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.47 tff(162,plain,
% 0.20/0.47 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (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_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (~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__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[161, 159])).
% 0.20/0.47 tff(163,plain,
% 0.20/0.47 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (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)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(164,plain,
% 0.20/0.47 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (~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__LE_(f(suc(suc(z))), s(s(s(|'0'|))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.20/0.47 tff(165,plain,
% 0.20/0.47 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[164, 60, 158])).
% 0.20/0.47 tff(166,plain,
% 0.20/0.47 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[165, 146])).
% 0.20/0.47 tff(167,assumption,(tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))), introduced(assumption)).
% 0.20/0.47 tff(168,assumption,(tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))), introduced(assumption)).
% 0.20/0.47 tff(169,plain,
% 0.20/0.47 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | 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))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(170,plain,
% 0.20/0.47 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (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))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(171,plain,
% 0.20/0.47 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | 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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.20/0.47 tff(172,plain,
% 0.20/0.47 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[171, 95, 168])).
% 0.20/0.47 tff(173,plain,
% 0.20/0.47 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[172, 167])).
% 0.20/0.47 tff(174,plain,
% 0.20/0.47 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~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))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(175,plain,
% 0.20/0.47 (((~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)))))) | (~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))))) | (~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(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(176,plain,
% 0.20/0.47 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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)))))) | (~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))))) | (~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(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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)))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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)))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[175])).
% 0.20/0.47 tff(177,plain,
% 0.20/0.47 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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)))))) | (~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))))) | (~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(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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)))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~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))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[176, 174])).
% 0.20/0.47 tff(178,plain,
% 0.20/0.47 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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)))))) | (~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))))) | (~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(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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)))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(179,plain,
% 0.20/0.47 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.47 tff(180,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[179, 135, 168, 167, 173])).
% 0.20/0.47 tff(181,plain,((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(182,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[181, 166, 155])).
% 0.20/0.47 tff(183,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(184,plain,
% 0.20/0.47 (^[B_247: $i] : refl((tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|)))))) <=> (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(185,plain,
% 0.20/0.48 (![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|)))))) <=> ![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[184])).
% 0.20/0.48 tff(186,plain,
% 0.20/0.48 (![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|)))))) <=> ![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(187,plain,
% 0.20/0.48 (^[B_247: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247)))) | tptp_fun__LE_(f(B_247), s(s(|'0'|)))) <=> (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(188,plain,
% 0.20/0.48 (![B_247: $i] : (((~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247)))) | tptp_fun__LE_(f(B_247), s(s(|'0'|)))) <=> ![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[187])).
% 0.20/0.48 tff(189,axiom,(![B_247: $i] : (((~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247)))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_476')).
% 0.20/0.48 tff(190,plain,
% 0.20/0.48 (![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.20/0.48 tff(191,plain,
% 0.20/0.48 (![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.20/0.48 tff(192,plain,(
% 0.20/0.48 ![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[191])).
% 0.20/0.48 tff(193,plain,
% 0.20/0.48 (![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[192, 185])).
% 0.20/0.48 tff(194,plain,
% 0.20/0.48 (((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), 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_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), 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'|))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(195,plain,
% 0.20/0.48 ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), 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'|))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(196,plain,
% 0.20/0.48 ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.20/0.48 tff(197,plain,
% 0.20/0.48 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[196, 193])).
% 0.20/0.48 tff(198,plain,
% 0.20/0.48 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[197, 183])).
% 0.20/0.48 tff(199,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[198, 145, 1])).
% 0.20/0.48 tff(200,plain,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(201,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))), introduced(assumption)).
% 0.20/0.48 tff(202,plain,
% 0.20/0.48 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[67, 201])).
% 0.20/0.48 tff(203,plain,
% 0.20/0.48 (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[84, 158])).
% 0.20/0.48 tff(204,plain,
% 0.20/0.48 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[203, 201])).
% 0.20/0.48 tff(205,plain,
% 0.20/0.48 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[102, 204, 202])).
% 0.20/0.48 tff(206,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[141, 135, 202, 204, 205])).
% 0.20/0.48 tff(207,plain,(tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(208,assumption,(~tptp_fun__LE_(f(z), s(s(s(|'0'|))))), introduced(assumption)).
% 0.20/0.48 tff(209,assumption,(~iLEQ(suc(z), suc(z))), introduced(assumption)).
% 0.20/0.48 tff(210,plain,
% 0.20/0.48 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(211,plain,
% 0.20/0.48 (tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[210, 47])).
% 0.20/0.48 tff(212,plain,
% 0.20/0.48 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (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_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | 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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(213,plain,
% 0.20/0.48 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (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)))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(214,plain,
% 0.20/0.48 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | 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))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.20/0.48 tff(215,plain,
% 0.20/0.48 (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))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[214, 60])).
% 0.20/0.48 tff(216,plain,
% 0.20/0.48 (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(z))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[215, 211])).
% 0.20/0.48 tff(217,plain,
% 0.20/0.48 (tptp_fun__E_(s(s(s(|'0'|))), f(z))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[216, 208])).
% 0.20/0.48 tff(218,plain,
% 0.20/0.48 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(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_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(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))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(219,plain,
% 0.20/0.48 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(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))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(220,plain,
% 0.20/0.48 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(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)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.20/0.48 tff(221,plain,
% 0.20/0.48 (tptp_fun__LE_(f(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)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[220, 80])).
% 0.20/0.48 tff(222,plain,
% 0.20/0.48 (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[221, 50])).
% 0.20/0.48 tff(223,plain,
% 0.20/0.48 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[222, 208])).
% 0.20/0.48 tff(224,plain,
% 0.20/0.48 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(225,plain,
% 0.20/0.48 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(226,plain,
% 0.20/0.48 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.20/0.48 tff(227,plain,
% 0.20/0.48 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[226, 95])).
% 0.20/0.48 tff(228,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[227, 223, 217, 209])).
% 0.20/0.48 tff(229,plain,(tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | iLEQ(suc(z), suc(z))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(230,plain,
% 0.20/0.48 (iLEQ(suc(z), suc(z))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[229, 208])).
% 0.20/0.48 tff(231,plain,
% 0.20/0.48 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(232,plain,
% 0.20/0.48 (((~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)))) | (~iLEQ(suc(z), suc(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(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(233,plain,
% 0.20/0.48 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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)))) | (~iLEQ(suc(z), suc(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(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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)))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[232])).
% 0.20/0.48 tff(234,plain,
% 0.20/0.48 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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)))) | (~iLEQ(suc(z), suc(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(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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)))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[233, 231])).
% 0.20/0.48 tff(235,plain,
% 0.20/0.48 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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)))) | (~iLEQ(suc(z), suc(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(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(236,plain,
% 0.20/0.48 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.20/0.48 tff(237,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[236, 135, 217, 223, 230])).
% 0.20/0.48 tff(238,plain,(tptp_fun__LE_(f(z), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.48 tff(239,assumption,(tptp_fun__LE_(f(z), s(s(s(|'0'|))))), introduced(assumption)).
% 0.20/0.48 tff(240,assumption,(~tptp_fun__LE_(f(z), s(s(|'0'|)))), introduced(assumption)).
% 0.20/0.48 tff(241,plain,
% 0.20/0.48 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z)))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(242,plain,
% 0.20/0.49 (((~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z))) <=> (tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[242])).
% 0.20/0.49 tff(244,plain,
% 0.20/0.49 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[243, 241])).
% 0.20/0.49 tff(245,plain,
% 0.20/0.49 ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(246,plain,
% 0.20/0.49 ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.49 tff(247,plain,
% 0.20/0.49 (tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(z))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[246, 31])).
% 0.20/0.49 tff(248,plain,
% 0.20/0.49 (tptp_fun__E_(s(s(|'0'|)), f(z))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[247, 240, 239])).
% 0.20/0.49 tff(249,assumption,(tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))), introduced(assumption)).
% 0.20/0.49 tff(250,plain,
% 0.20/0.49 (((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), 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_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), 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'|))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(251,plain,
% 0.20/0.49 ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), 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'|))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(252,plain,
% 0.20/0.49 ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), 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'|)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.49 tff(253,plain,
% 0.20/0.49 (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'|)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[252, 193])).
% 0.20/0.49 tff(254,plain,
% 0.20/0.49 (tptp_fun__E_(s(s(|'0'|)), f(suc(z)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[253, 240, 249])).
% 0.20/0.49 tff(255,plain,
% 0.20/0.49 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(256,plain,
% 0.20/0.49 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(257,plain,
% 0.20/0.49 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.20/0.49 tff(258,plain,
% 0.20/0.49 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[257, 13])).
% 0.20/0.49 tff(259,plain,
% 0.20/0.49 (iLEQ(suc(z), suc(z))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[258, 254, 248])).
% 0.20/0.49 tff(260,plain,
% 0.20/0.49 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(261,plain,
% 0.20/0.49 (((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(262,plain,
% 0.20/0.49 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[261])).
% 0.20/0.49 tff(263,plain,
% 0.20/0.49 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[262, 260])).
% 0.20/0.49 tff(264,plain,
% 0.20/0.49 ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(265,plain,
% 0.20/0.49 ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.20/0.49 tff(266,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[265, 115, 248, 254, 259])).
% 0.20/0.49 tff(267,plain,(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(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(268,plain,
% 0.20/0.49 (tptp_fun__LE_(f(z), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[267, 238])).
% 0.20/0.49 tff(269,plain,
% 0.20/0.49 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[268, 207])).
% 0.20/0.49 tff(270,assumption,(tptp_fun__LE_(f(z), s(s(|'0'|)))), introduced(assumption)).
% 0.20/0.49 tff(271,assumption,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 0.20/0.49 tff(272,assumption,(tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), introduced(assumption)).
% 0.20/0.49 tff(273,assumption,(~tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 0.20/0.49 tff(274,plain,
% 0.20/0.49 (^[B_291: $i] : refl((tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|))))) <=> (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(275,plain,
% 0.20/0.49 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|))))) <=> ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[274])).
% 0.20/0.49 tff(276,plain,
% 0.20/0.49 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|))))) <=> ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(277,plain,
% 0.20/0.49 (^[B_291: $i] : rewrite((((~tptp_fun__LE_(f(B_291), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|))) <=> (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(278,plain,
% 0.20/0.49 (![B_291: $i] : (((~tptp_fun__LE_(f(B_291), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|))) <=> ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[277])).
% 0.20/0.49 tff(279,axiom,(![B_291: $i] : (((~tptp_fun__LE_(f(B_291), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_44')).
% 0.20/0.49 tff(280,plain,
% 0.20/0.49 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.20/0.49 tff(281,plain,
% 0.20/0.49 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[280, 276])).
% 0.20/0.49 tff(282,plain,(
% 0.20/0.49 ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[281])).
% 0.20/0.49 tff(283,plain,
% 0.20/0.49 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[282, 275])).
% 0.20/0.49 tff(284,plain,
% 0.20/0.49 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(285,plain,
% 0.20/0.49 ((tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))) <=> (tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(286,plain,
% 0.20/0.49 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[285])).
% 0.20/0.49 tff(287,plain,
% 0.20/0.49 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[286, 284])).
% 0.20/0.49 tff(288,plain,
% 0.20/0.49 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(289,plain,
% 0.20/0.49 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.20/0.49 tff(290,plain,
% 0.20/0.49 (tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[289, 283])).
% 0.20/0.49 tff(291,plain,
% 0.20/0.49 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[290, 271, 273])).
% 0.20/0.49 tff(292,plain,
% 0.20/0.49 (^[B_309: $i] : refl((tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(293,plain,
% 0.20/0.49 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> ![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[292])).
% 0.20/0.49 tff(294,plain,
% 0.20/0.49 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> ![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(295,plain,
% 0.20/0.49 (^[B_309: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_309)))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(296,plain,
% 0.20/0.49 (![B_309: $i] : (((~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_309)))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> ![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[295])).
% 0.20/0.49 tff(297,axiom,(![B_309: $i] : (((~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_309)))) | tptp_fun__LE_(f(B_309), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_547')).
% 0.20/0.49 tff(298,plain,
% 0.20/0.49 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.20/0.49 tff(299,plain,
% 0.20/0.49 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.20/0.49 tff(300,plain,(
% 0.20/0.49 ![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 0.20/0.49 inference(skolemize,[status(sab)],[299])).
% 0.20/0.49 tff(301,plain,
% 0.20/0.49 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[300, 293])).
% 0.20/0.49 tff(302,plain,
% 0.20/0.49 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(303,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_287')).
% 0.20/0.49 tff(304,plain,
% 0.20/0.49 (~tptp_fun__LE_(f(z), |'0'|)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.20/0.49 tff(305,plain,
% 0.20/0.49 (((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))) <=> ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(306,plain,
% 0.20/0.49 ((tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|)) <=> (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(307,plain,
% 0.20/0.49 (((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|))) <=> ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[306])).
% 0.20/0.50 tff(308,plain,
% 0.20/0.50 (((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|))) <=> ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[307, 305])).
% 0.20/0.50 tff(309,plain,
% 0.20/0.50 ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(310,plain,
% 0.20/0.50 ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(suc(B_309))) | (~tptp_fun__LE_(f(suc(B_309)), s(|'0'|))) | tptp_fun__LE_(f(B_309), |'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.20/0.50 tff(311,plain,
% 0.20/0.50 (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[310, 304, 301])).
% 0.20/0.50 tff(312,plain,
% 0.20/0.50 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[311, 291])).
% 0.20/0.50 tff(313,plain,
% 0.20/0.50 (^[B_291: $i] : refl((tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|))))) <=> (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(314,plain,
% 0.20/0.50 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|))))) <=> ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[313])).
% 0.20/0.50 tff(315,plain,
% 0.20/0.50 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|))))) <=> ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(316,plain,
% 0.20/0.50 (^[B_291: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_291)))) | tptp_fun__LE_(f(B_291), s(|'0'|))) <=> (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(317,plain,
% 0.20/0.50 (![B_291: $i] : (((~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_291)))) | tptp_fun__LE_(f(B_291), s(|'0'|))) <=> ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[316])).
% 0.20/0.50 tff(318,axiom,(![B_291: $i] : (((~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_291)))) | tptp_fun__LE_(f(B_291), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_222')).
% 0.20/0.50 tff(319,plain,
% 0.20/0.50 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.20/0.50 tff(320,plain,
% 0.20/0.50 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[319, 315])).
% 0.20/0.50 tff(321,plain,(
% 0.20/0.50 ![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[320])).
% 0.20/0.50 tff(322,plain,
% 0.20/0.50 (![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[321, 314])).
% 0.20/0.50 tff(323,plain,
% 0.20/0.50 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), 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_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), 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'|)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(324,plain,
% 0.20/0.50 ((tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), 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'|)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(325,plain,
% 0.20/0.50 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), 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'|))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[324])).
% 0.20/0.50 tff(326,plain,
% 0.20/0.50 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), 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'|)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[325, 323])).
% 0.20/0.50 tff(327,plain,
% 0.20/0.50 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(328,plain,
% 0.20/0.50 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), 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'|))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.20/0.50 tff(329,plain,
% 0.20/0.50 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[328, 322])).
% 0.20/0.50 tff(330,plain,
% 0.20/0.50 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[329, 271, 273])).
% 0.20/0.50 tff(331,plain,
% 0.20/0.50 (^[B_309: $i] : refl((tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|)))) <=> (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(332,plain,
% 0.20/0.50 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|)))) <=> ![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[331])).
% 0.20/0.50 tff(333,plain,
% 0.20/0.50 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|)))) <=> ![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(334,plain,
% 0.20/0.50 (^[B_309: $i] : rewrite((((~tptp_fun__LE_(f(B_309), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_309))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(335,plain,
% 0.20/0.50 (![B_309: $i] : (((~tptp_fun__LE_(f(B_309), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_309))) | tptp_fun__LE_(f(B_309), |'0'|)) <=> ![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[334])).
% 0.20/0.50 tff(336,axiom,(![B_309: $i] : (((~tptp_fun__LE_(f(B_309), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_309))) | tptp_fun__LE_(f(B_309), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_89')).
% 0.20/0.50 tff(337,plain,
% 0.20/0.50 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.20/0.50 tff(338,plain,
% 0.20/0.50 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[337, 333])).
% 0.20/0.50 tff(339,plain,(
% 0.20/0.50 ![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[338])).
% 0.20/0.50 tff(340,plain,
% 0.20/0.50 (![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[339, 332])).
% 0.20/0.50 tff(341,plain,
% 0.20/0.50 (((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(342,plain,
% 0.20/0.50 ((tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|)))) <=> (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(343,plain,
% 0.20/0.50 (((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[342])).
% 0.20/0.50 tff(344,plain,
% 0.20/0.50 (((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[343, 341])).
% 0.20/0.50 tff(345,plain,
% 0.20/0.50 ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(346,plain,
% 0.20/0.50 ((~![B_309: $i] : (tptp_fun__E_(|'0'|, f(B_309)) | tptp_fun__LE_(f(B_309), |'0'|) | (~tptp_fun__LE_(f(B_309), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.20/0.50 tff(347,plain,
% 0.20/0.50 (tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[346, 304, 340])).
% 0.20/0.50 tff(348,plain,
% 0.20/0.50 (tptp_fun__E_(|'0'|, f(z))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[347, 330])).
% 0.20/0.50 tff(349,plain,
% 0.20/0.50 (^[A_4: $i] : refl((iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(350,plain,
% 0.20/0.50 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[349])).
% 0.20/0.50 tff(351,plain,
% 0.20/0.50 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(352,plain,
% 0.20/0.50 (^[A_4: $i] : rewrite((((~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | iLEQ(suc(A_4), suc(A_4))) <=> (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(353,plain,
% 0.20/0.50 (![A_4: $i] : (((~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'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_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[352])).
% 0.20/0.50 tff(354,axiom,(![A_4: $i] : (((~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | iLEQ(suc(A_4), suc(A_4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_469')).
% 0.20/0.50 tff(355,plain,
% 0.20/0.50 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.20/0.50 tff(356,plain,
% 0.20/0.50 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[355, 351])).
% 0.20/0.50 tff(357,plain,(
% 0.20/0.50 ![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[356])).
% 0.20/0.50 tff(358,plain,
% 0.20/0.50 (![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[357, 350])).
% 0.20/0.50 tff(359,plain,
% 0.20/0.50 (((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))) <=> ((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(360,plain,
% 0.20/0.50 ((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(361,plain,
% 0.20/0.50 ((~![A_4: $i] : (iLEQ(suc(A_4), suc(A_4)) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(A_4))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.20/0.50 tff(362,plain,
% 0.20/0.50 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[361, 358])).
% 0.20/0.50 tff(363,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[362, 348, 312, 209])).
% 0.20/0.50 tff(364,plain,((~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(s(|'0'|), f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(365,plain,
% 0.20/0.50 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[364, 209, 271])).
% 0.20/0.50 tff(366,plain,
% 0.20/0.50 (^[A_3: $i] : refl((iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(367,plain,
% 0.20/0.50 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[366])).
% 0.20/0.50 tff(368,plain,
% 0.20/0.50 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(369,plain,
% 0.20/0.50 (^[A_3: $i] : rewrite((((~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | iLEQ(suc(A_3), suc(A_3))) <=> (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(370,plain,
% 0.20/0.50 (![A_3: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(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(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[369])).
% 0.20/0.50 tff(371,axiom,(![A_3: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | iLEQ(suc(A_3), suc(A_3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_398')).
% 0.20/0.50 tff(372,plain,
% 0.20/0.50 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[371, 370])).
% 0.20/0.50 tff(373,plain,
% 0.20/0.50 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[372, 368])).
% 0.20/0.50 tff(374,plain,(
% 0.20/0.50 ![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[373])).
% 0.20/0.50 tff(375,plain,
% 0.20/0.50 (![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[374, 367])).
% 0.20/0.50 tff(376,plain,
% 0.20/0.50 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(377,plain,
% 0.20/0.50 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(378,plain,
% 0.20/0.50 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.20/0.50 tff(379,plain,
% 0.20/0.50 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[378, 375])).
% 0.20/0.50 tff(380,plain,
% 0.20/0.50 (~tptp_fun__E_(s(|'0'|), f(z))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[379, 365, 209])).
% 0.20/0.50 tff(381,plain,
% 0.20/0.50 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(382,plain,
% 0.20/0.50 ((tptp_fun__E_(s(|'0'|), f(z)) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(383,plain,
% 0.20/0.50 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(z)) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[382])).
% 0.20/0.50 tff(384,plain,
% 0.20/0.50 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(z)) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[383, 381])).
% 0.20/0.50 tff(385,plain,
% 0.20/0.50 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(z)) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(386,plain,
% 0.20/0.50 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(B_291)) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(B_291), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.20/0.50 tff(387,plain,
% 0.20/0.50 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[386, 283])).
% 0.20/0.50 tff(388,plain,
% 0.20/0.50 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[387, 380, 270])).
% 0.20/0.50 tff(389,plain,
% 0.20/0.50 (tptp_fun__E_(|'0'|, f(z))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[347, 388])).
% 0.20/0.50 tff(390,assumption,(tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 0.20/0.50 tff(391,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 0.20/0.50 tff(392,plain,
% 0.20/0.50 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | ((~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_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(393,plain,
% 0.20/0.50 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(394,plain,
% 0.20/0.50 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[393])).
% 0.20/0.51 tff(395,plain,
% 0.20/0.51 (((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[394, 392])).
% 0.20/0.51 tff(396,plain,
% 0.20/0.51 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(397,plain,
% 0.20/0.51 ((~![A_3: $i] : (iLEQ(suc(A_3), suc(A_3)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.20/0.51 tff(398,plain,
% 0.20/0.51 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[397, 375])).
% 0.20/0.51 tff(399,plain,
% 0.20/0.51 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[398, 391, 390])).
% 0.20/0.51 tff(400,plain,
% 0.20/0.51 (^[B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : refl(((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(401,plain,
% 0.20/0.51 (![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) <=> ![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[400])).
% 0.20/0.51 tff(402,plain,
% 0.20/0.51 (![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) <=> ![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(403,plain,
% 0.20/0.51 (^[B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(A_3), suc(B_292)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(A_3), suc(B_292)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(B_294), suc(B_295)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(B_294), suc(B_295)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), (((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) | (~iLEQ(suc(B_293), suc(B_294)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(B_293), suc(B_294)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(B_293), suc(B_294)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) | (~iLEQ(suc(B_293), suc(B_294)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) | (~iLEQ(suc(B_293), suc(B_294)))) | (~iLEQ(suc(B_292), suc(B_293)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(B_292), suc(B_293)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294))))) | (~iLEQ(suc(B_292), suc(B_293)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))), (((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) | (~iLEQ(suc(B_293), suc(B_294)))) | (~iLEQ(suc(B_292), suc(B_293)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(404,plain,
% 0.20/0.52 (![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) | (~iLEQ(suc(B_293), suc(B_294)))) | (~iLEQ(suc(B_292), suc(B_293)))) <=> ![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[403])).
% 0.20/0.52 tff(405,axiom,(![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_294)))) | (~tptp_fun__E_(s(|'0'|), f(B_292)))) | (~iLEQ(suc(A_3), suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(B_293)))) | (~iLEQ(suc(B_294), suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293))))) | (~iLEQ(suc(B_293), suc(B_294)))) | (~iLEQ(suc(B_292), suc(B_293))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_151')).
% 0.20/0.52 tff(406,plain,
% 0.20/0.52 (![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.20/0.52 tff(407,plain,
% 0.20/0.52 (![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[406, 402])).
% 0.20/0.52 tff(408,plain,(
% 0.20/0.52 ![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[407])).
% 0.20/0.52 tff(409,plain,
% 0.20/0.52 (![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[408, 401])).
% 0.20/0.52 tff(410,plain,
% 0.20/0.52 (((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(411,plain,
% 0.20/0.52 (((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(412,plain,
% 0.20/0.52 (((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[411])).
% 0.20/0.52 tff(413,plain,
% 0.20/0.52 (((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[412, 410])).
% 0.20/0.52 tff(414,plain,
% 0.20/0.52 ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(415,plain,
% 0.20/0.52 ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[414, 413])).
% 0.20/0.52 tff(416,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[415, 409, 390, 391, 399])).
% 0.20/0.52 tff(417,plain,((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(418,plain,
% 0.20/0.52 (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[417, 365])).
% 0.20/0.52 tff(419,plain,
% 0.20/0.52 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), 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_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), 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'|)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(420,plain,
% 0.20/0.52 ((tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), 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'|)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(421,plain,
% 0.20/0.52 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), 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'|))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[420])).
% 0.20/0.52 tff(422,plain,
% 0.20/0.52 (((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))) <=> ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), 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'|)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[421, 419])).
% 0.20/0.52 tff(423,plain,
% 0.20/0.52 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(424,plain,
% 0.20/0.52 ((~![B_291: $i] : (tptp_fun__E_(s(|'0'|), f(suc(B_291))) | tptp_fun__LE_(f(B_291), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_291)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.20/0.52 tff(425,plain,
% 0.20/0.52 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[424, 322])).
% 0.20/0.52 tff(426,plain,
% 0.20/0.52 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[425, 418, 272])).
% 0.20/0.52 tff(427,plain,
% 0.20/0.52 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[311, 426])).
% 0.20/0.52 tff(428,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[362, 427, 389, 209])).
% 0.20/0.52 tff(429,plain,(iLEQ(suc(z), suc(z)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(430,plain,
% 0.20/0.52 (iLEQ(suc(z), suc(z))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[429, 270, 272, 271])).
% 0.20/0.52 tff(431,plain,
% 0.20/0.52 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[290, 273, 271])).
% 0.20/0.52 tff(432,plain,
% 0.20/0.52 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[311, 431])).
% 0.20/0.52 tff(433,plain,
% 0.20/0.52 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[329, 273, 271])).
% 0.20/0.52 tff(434,plain,
% 0.20/0.52 (tptp_fun__E_(|'0'|, f(z))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[347, 433])).
% 0.20/0.52 tff(435,assumption,(iLEQ(suc(z), suc(z))), introduced(assumption)).
% 0.20/0.52 tff(436,plain,
% 0.20/0.52 (^[B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : refl(((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(437,plain,
% 0.20/0.52 (![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) <=> ![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[436])).
% 0.20/0.52 tff(438,plain,
% 0.20/0.52 (![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) <=> ![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(439,plain,
% 0.20/0.52 (^[B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_311)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) <=> ((~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) <=> ((~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) <=> (((~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_310)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_312)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_312)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_313)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(B_311), suc(B_312)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(B_311), suc(B_312)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(B_310), suc(B_311)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(B_310), suc(B_311)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(A_4), suc(B_310)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(A_4), suc(B_310)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~iLEQ(suc(B_312), suc(B_313)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(B_312), suc(B_313)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~iLEQ(suc(B_312), suc(B_313)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~iLEQ(suc(B_312), suc(B_313)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~iLEQ(suc(B_312), suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(A_4)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310))))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~iLEQ(suc(B_312), suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(440,plain,
% 0.20/0.53 (![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~iLEQ(suc(B_312), suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[439])).
% 0.20/0.53 tff(441,axiom,(![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(B_311))))) | (~tptp_fun__E_(|'0'|, f(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_313))))) | (~tptp_fun__E_(|'0'|, f(B_310)))) | (~tptp_fun__E_(|'0'|, f(B_312)))) | (~tptp_fun__E_(|'0'|, f(suc(B_312))))) | (~tptp_fun__E_(|'0'|, f(B_313)))) | (~iLEQ(suc(B_311), suc(B_312)))) | (~iLEQ(suc(B_310), suc(B_311)))) | (~iLEQ(suc(A_4), suc(B_310)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~iLEQ(suc(B_312), suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(A_4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_442')).
% 0.20/0.53 tff(442,plain,
% 0.20/0.53 (![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.20/0.53 tff(443,plain,
% 0.20/0.53 (![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[442, 438])).
% 0.20/0.53 tff(444,plain,(
% 0.20/0.53 ![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[443])).
% 0.20/0.53 tff(445,plain,
% 0.20/0.53 (![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[444, 437])).
% 0.20/0.53 tff(446,plain,
% 0.20/0.53 (((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(447,plain,
% 0.20/0.53 (((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(448,plain,
% 0.20/0.53 (((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[447])).
% 0.20/0.54 tff(449,plain,
% 0.20/0.54 (((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[448, 446])).
% 0.20/0.54 tff(450,plain,
% 0.20/0.54 ((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(451,plain,
% 0.20/0.54 ((~![B_310: $i, A_4: $i, B_311: $i, B_312: $i, B_313: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_313)))) | (~tptp_fun__E_(|'0'|, f(B_313))) | (~iLEQ(suc(B_311), suc(B_312))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~iLEQ(suc(B_312), suc(B_313))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~iLEQ(suc(A_4), suc(B_310))) | (~iLEQ(suc(B_310), suc(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_312)))) | (~tptp_fun__E_(|'0'|, f(B_312))) | (~tptp_fun__E_(|'0'|, f(B_310))) | (~tptp_fun__E_(|'0'|, f(B_311))) | (~tptp_fun__E_(|'0'|, f(suc(B_311)))) | (~tptp_fun__E_(|'0'|, f(suc(B_310)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[450, 449])).
% 0.20/0.54 tff(452,plain,
% 0.20/0.54 ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[451, 445, 435])).
% 0.20/0.54 tff(453,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[452, 434, 432])).
% 0.20/0.54 tff(454,plain,(tptp_fun__E_(s(|'0'|), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(455,plain,
% 0.20/0.54 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[454, 430, 271])).
% 0.20/0.54 tff(456,assumption,(tptp_fun__E_(s(|'0'|), f(z))), introduced(assumption)).
% 0.20/0.54 tff(457,plain,
% 0.20/0.54 (iLEQ(suc(z), suc(z))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[379, 390, 456])).
% 0.20/0.54 tff(458,plain,
% 0.20/0.54 (((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(459,plain,
% 0.20/0.54 (((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(460,plain,
% 0.20/0.54 (((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[459])).
% 0.20/0.54 tff(461,plain,
% 0.20/0.54 (((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[460, 458])).
% 0.20/0.54 tff(462,plain,
% 0.20/0.54 ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(463,plain,
% 0.20/0.54 ((~![B_292: $i, B_293: $i, B_295: $i, B_294: $i, A_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~iLEQ(suc(A_3), suc(B_292))) | (~iLEQ(suc(B_292), suc(B_293))) | (~iLEQ(suc(B_293), suc(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_293)))) | (~iLEQ(suc(B_294), suc(B_295))) | (~tptp_fun__E_(s(|'0'|), f(B_293))) | (~tptp_fun__E_(s(|'0'|), f(B_292))) | (~tptp_fun__E_(s(|'0'|), f(B_294))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_292)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_295)))) | (~tptp_fun__E_(s(|'0'|), f(B_295))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_294)))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[462, 461])).
% 0.20/0.54 tff(464,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[463, 409, 456, 390, 457])).
% 0.20/0.54 tff(465,plain,((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(466,plain,
% 0.20/0.54 (~tptp_fun__E_(s(|'0'|), f(z))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[465, 455])).
% 0.20/0.54 tff(467,plain,
% 0.20/0.54 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[387, 466, 270])).
% 0.20/0.54 tff(468,plain,
% 0.20/0.54 (tptp_fun__E_(|'0'|, f(z))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[347, 467])).
% 0.20/0.54 tff(469,plain,
% 0.20/0.54 (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[417, 455])).
% 0.20/0.54 tff(470,plain,
% 0.20/0.54 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[425, 469, 272])).
% 0.20/0.54 tff(471,plain,
% 0.20/0.54 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[311, 470])).
% 0.20/0.54 tff(472,plain,
% 0.20/0.54 ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[451, 445, 430])).
% 0.20/0.54 tff(473,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[472, 471, 468])).
% 0.20/0.54 tff(474,plain,((~tptp_fun__LE_(f(z), s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(475,plain,
% 0.20/0.54 (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[474, 269, 200])).
% 0.20/0.54 tff(476,plain,
% 0.20/0.54 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | (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_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | 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'|))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(477,plain,
% 0.20/0.54 (((~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(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(478,plain,
% 0.20/0.54 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~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)))))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | (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'|)))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[477])).
% 0.20/0.54 tff(479,plain,
% 0.20/0.54 (((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~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)))))) <=> ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | 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'|))))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[478, 476])).
% 0.20/0.54 tff(480,plain,
% 0.20/0.54 ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | ((~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)))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(481,plain,
% 0.20/0.54 ((~![B_247: $i] : ((~tptp_fun__LE_(f(B_247), s(s(s(|'0'|))))) | tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_247)))) | 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'|)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[480, 479])).
% 0.20/0.54 tff(482,plain,
% 0.20/0.54 (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'|)))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[481, 31])).
% 0.20/0.54 tff(483,plain,
% 0.20/0.54 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[482, 183])).
% 0.20/0.54 tff(484,plain,
% 0.20/0.54 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[483, 475])).
% 0.20/0.54 tff(485,assumption,(tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))), introduced(assumption)).
% 0.20/0.54 tff(486,plain,
% 0.20/0.54 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | ((~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)))))) <=> ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (~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)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(487,plain,
% 0.20/0.54 ((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)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(488,plain,
% 0.20/0.54 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (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_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | ((~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))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[487])).
% 0.20/0.54 tff(489,plain,
% 0.20/0.54 (((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (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_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (~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)))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[488, 486])).
% 0.20/0.54 tff(490,plain,
% 0.20/0.54 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (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))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(491,plain,
% 0.20/0.54 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))) | (~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))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.20/0.54 tff(492,plain,
% 0.20/0.54 ((~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))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[491, 13])).
% 0.20/0.54 tff(493,plain,
% 0.20/0.54 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[492, 485, 2])).
% 0.20/0.54 tff(494,plain,
% 0.20/0.54 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~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_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~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))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(495,plain,
% 0.20/0.54 (((~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))))) | (~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)))))) | (~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)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z))))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(496,plain,
% 0.20/0.54 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~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))))) | (~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)))))) | (~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)))))) | (~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)))))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~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)))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[495])).
% 0.20/0.55 tff(497,plain,
% 0.20/0.55 (((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~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))))) | (~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)))))) | (~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)))))) | (~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)))))))) <=> ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~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))))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[496, 494])).
% 0.20/0.55 tff(498,plain,
% 0.20/0.55 ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | ((~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))))) | (~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)))))) | (~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)))))) | (~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)))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(499,plain,
% 0.20/0.55 ((~![B_249: $i, B_251: $i, A_2: $i, B_250: $i, B_248: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_248)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_248))) | (~iLEQ(suc(B_250), suc(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_249))) | (~iLEQ(suc(B_248), suc(B_249))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_250)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_251))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_249), suc(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_251)))) | (~iLEQ(suc(A_2), suc(B_248))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_250))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_249)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.20/0.55 tff(500,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[499, 115, 2, 485, 493])).
% 0.20/0.55 tff(501,plain,((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(502,plain,
% 0.20/0.55 (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[501, 484])).
% 0.20/0.55 tff(503,plain,
% 0.20/0.55 (((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), 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_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), 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'|))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(504,plain,
% 0.20/0.55 ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), 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'|))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(505,plain,
% 0.20/0.55 ((~![B_247: $i] : (tptp_fun__LE_(f(B_247), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_247))) | (~tptp_fun__LE_(f(suc(B_247)), 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'|)))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.20/0.55 tff(506,plain,
% 0.20/0.55 (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'|)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[505, 193])).
% 0.20/0.55 tff(507,plain,
% 0.20/0.55 (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[506, 502, 475])).
% 0.20/0.55 tff(508,plain,
% 0.20/0.55 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | ((~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__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (~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__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(509,plain,
% 0.20/0.55 ((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__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__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(510,plain,
% 0.20/0.55 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (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_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | ((~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__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[509])).
% 0.20/0.55 tff(511,plain,
% 0.20/0.55 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (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_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (~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__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[510, 508])).
% 0.20/0.55 tff(512,plain,
% 0.20/0.55 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (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))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(513,plain,
% 0.20/0.55 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_158), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_158)))) | (~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__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[512, 511])).
% 0.20/0.55 tff(514,plain,
% 0.20/0.55 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[513, 60, 150])).
% 0.20/0.55 tff(515,plain,
% 0.20/0.55 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[514, 507])).
% 0.20/0.55 tff(516,assumption,(~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.20/0.55 tff(517,plain,
% 0.20/0.55 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(518,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[517, 47, 516])).
% 0.20/0.55 tff(519,plain,(tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(520,plain,
% 0.20/0.55 (((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))) <=> ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(521,plain,
% 0.20/0.55 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(522,plain,
% 0.20/0.55 ((~![B_158: $i] : (tptp_fun__LE_(f(B_158), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(B_158)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_158))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[521, 520])).
% 0.20/0.55 tff(523,plain,
% 0.20/0.55 (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[522, 80])).
% 0.20/0.55 tff(524,plain,
% 0.20/0.55 (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))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[523, 519])).
% 0.20/0.55 tff(525,plain,
% 0.20/0.55 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[524, 507])).
% 0.20/0.55 tff(526,assumption,(tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))), introduced(assumption)).
% 0.20/0.55 tff(527,plain,
% 0.20/0.55 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | ((~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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~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))))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(528,plain,
% 0.20/0.55 ((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))))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(529,plain,
% 0.20/0.55 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | ((~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)))))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[528])).
% 0.20/0.55 tff(530,plain,
% 0.20/0.55 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (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_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~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))))))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[529, 527])).
% 0.20/0.55 tff(531,plain,
% 0.20/0.55 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (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)))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(532,plain,
% 0.20/0.55 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))))) | (~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)))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.20/0.55 tff(533,plain,
% 0.20/0.55 (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[532, 95, 167])).
% 0.20/0.55 tff(534,plain,
% 0.20/0.55 (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[533, 526])).
% 0.20/0.55 tff(535,plain,
% 0.20/0.55 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~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)))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(536,plain,
% 0.20/0.55 (((~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))))))) | (~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)))))) | (~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(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)))))) | (~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(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(537,plain,
% 0.20/0.56 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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))))))) | (~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)))))) | (~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(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)))))) | (~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))))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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))))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[536])).
% 0.20/0.56 tff(538,plain,
% 0.20/0.56 (((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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))))))) | (~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)))))) | (~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(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)))))) | (~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))))))))) <=> ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~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)))))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[537, 535])).
% 0.20/0.56 tff(539,plain,
% 0.20/0.56 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | ((~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))))))) | (~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)))))) | (~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(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)))))) | (~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))))))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(540,plain,
% 0.20/0.56 ((~![B_160: $i, B_162: $i, A_1: $i, B_159: $i, B_161: $i] : ((~iLEQ(suc(A_1), suc(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_160)))) | (~iLEQ(suc(B_161), suc(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_161)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(B_159), suc(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_160))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_159))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_162)))) | (~iLEQ(suc(B_160), suc(B_161))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_162))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_159)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[539, 538])).
% 0.20/0.56 tff(541,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[540, 135, 167, 526, 534])).
% 0.20/0.56 tff(542,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,[]))).
% 0.20/0.56 tff(543,plain,
% 0.20/0.56 ($false),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[542, 525, 515])).
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56 % E exiting
%------------------------------------------------------------------------------