%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO680-1 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 0.11s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO680-1 : TPTP v9.0.0. Released v7.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n016.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 13:22:32 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(tptp_fun__LE__type, type, (
% 0.11/0.38 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.11/0.38 tff(s_type, type, (
% 0.11/0.38 s: $i > $i)).
% 0.11/0.38 tff(tptp_fun__0__type, type, (
% 0.11/0.38 tptp_fun__0_: $i)).
% 0.11/0.38 tff(f_type, type, (
% 0.11/0.38 f: $i > $i)).
% 0.11/0.38 tff(z_type, type, (
% 0.11/0.38 z: $i)).
% 0.11/0.38 tff(tptp_fun__E__type, type, (
% 0.11/0.38 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.11/0.38 tff(suc_type, type, (
% 0.11/0.38 suc: $i > $i)).
% 0.11/0.38 tff(iLEQ_type, type, (
% 0.11/0.38 iLEQ: ( $i * $i ) > $o)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(s(s(s(|'0'|))))) <=> tptp_fun__LE_(f(A), s(s(s(s(|'0'|))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|))))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|))))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(4,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_104')).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.38 tff(6,plain,(
% 0.11/0.38 ![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[5])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.38 tff(10,assumption,(~tptp_fun__LE_(f(z), s(s(s(|'0'|))))), introduced(assumption)).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 (^[B_23: $i] : refl((tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|))))))) <=> (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|))))))) <=> ![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[11])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|))))))) <=> ![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (^[B_23: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23)))) | tptp_fun__LE_(f(B_23), s(s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|))))))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 (![B_23: $i] : (((~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23)))) | tptp_fun__LE_(f(B_23), s(s(s(|'0'|))))) <=> ![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.11/0.38 tff(16,axiom,(![B_23: $i] : (((~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23)))) | tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_102')).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 (![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.11/0.38 tff(19,plain,(
% 0.11/0.38 ![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))),
% 0.11/0.38 inference(skolemize,[status(sab)],[18])).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))))) <=> ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|))))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[24, 10, 9])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(27,plain,
% 0.11/0.38 (tptp_fun__LE_(f(z), s(s(s(s(|'0'|)))))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[26, 7])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (^[B_23: $i] : refl((tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23))) <=> (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23))) <=> ![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23))) <=> ![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (^[B_23: $i] : rewrite((((~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23))) | tptp_fun__LE_(f(B_23), s(s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (![B_23: $i] : (((~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23))) | tptp_fun__LE_(f(B_23), s(s(s(|'0'|))))) <=> ![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[31])).
% 0.11/0.39 tff(33,axiom,(![B_23: $i] : (((~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23))) | tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_127')).
% 0.11/0.39 tff(34,plain,
% 0.11/0.39 (![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.39 tff(35,plain,
% 0.11/0.39 (![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.11/0.39 tff(36,plain,(
% 0.11/0.39 ![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[35])).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 (![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[36, 29])).
% 0.11/0.39 tff(38,plain,
% 0.11/0.39 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (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_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | 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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(39,plain,
% 0.11/0.39 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (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)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(40,plain,
% 0.11/0.39 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | 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))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.11/0.39 tff(41,plain,
% 0.11/0.39 (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))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.11/0.39 tff(42,plain,
% 0.11/0.39 (tptp_fun__LE_(f(z), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(z))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[41, 27])).
% 0.11/0.39 tff(43,plain,
% 0.11/0.39 (tptp_fun__E_(s(s(s(|'0'|))), f(z))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[42, 10])).
% 0.11/0.39 tff(44,assumption,(tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))), introduced(assumption)).
% 0.11/0.39 tff(45,assumption,(tptp_fun__E_(s(s(s(|'0'|))), f(z))), introduced(assumption)).
% 0.11/0.39 tff(46,plain,
% 0.11/0.39 (^[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)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(47,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[46])).
% 0.11/0.39 tff(48,plain,
% 0.11/0.39 (![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(49,plain,
% 0.19/0.39 (^[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)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(50,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.39 tff(51,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/sandbox2/benchmark/theBenchmark.p','clause_14')).
% 0.19/0.39 tff(52,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.19/0.39 tff(53,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.19/0.39 tff(54,plain,(
% 0.19/0.39 ![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))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[53])).
% 0.19/0.39 tff(55,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.19/0.39 tff(56,plain,
% 0.19/0.39 (((~![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(57,plain,
% 0.19/0.39 ((~![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))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(58,plain,
% 0.19/0.39 ((~![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)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.39 tff(59,plain,
% 0.19/0.39 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[58, 55])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (iLEQ(suc(z), suc(z))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[59, 45, 44])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (^[B_25: $i, A_1: $i, B_24: $i] : refl(((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) <=> ![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) <=> ![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (^[B_25: $i, A_1: $i, B_24: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))), (((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) | (~iLEQ(suc(A_1), suc(B_24)))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) | (~iLEQ(suc(A_1), suc(B_24)))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) | (~iLEQ(suc(A_1), suc(B_24)))) <=> ((~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))), (((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) | (~iLEQ(suc(A_1), suc(B_24)))) <=> ((~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))))), ((((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) | (~iLEQ(suc(A_1), suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> (((~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))))), rewrite((((~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))), ((((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) | (~iLEQ(suc(A_1), suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))))), (((((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) | (~iLEQ(suc(A_1), suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24))))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24))))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))), (((((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) | (~iLEQ(suc(A_1), suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))))), ((((((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) | (~iLEQ(suc(A_1), suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25))))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25))))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))), ((((((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) | (~iLEQ(suc(A_1), suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))))), (((((((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) | (~iLEQ(suc(A_1), suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25)))) | (~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_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))), (((((((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) | (~iLEQ(suc(A_1), suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25))))) | (~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_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(65,plain,
% 0.19/0.40 (![B_25: $i, A_1: $i, B_24: $i] : ((((((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) | (~iLEQ(suc(A_1), suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1))))) <=> ![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[64])).
% 0.19/0.40 tff(66,axiom,(![B_25: $i, A_1: $i, B_24: $i] : ((((((((~iLEQ(suc(B_24), suc(B_25))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24)))) | (~iLEQ(suc(A_1), suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_71')).
% 0.19/0.40 tff(67,plain,
% 0.19/0.40 (![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.19/0.40 tff(68,plain,
% 0.19/0.40 (![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.19/0.40 tff(69,plain,(
% 0.19/0.40 ![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[68])).
% 0.19/0.40 tff(70,plain,
% 0.19/0.40 (![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.19/0.40 tff(71,plain,
% 0.19/0.40 (((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(72,plain,
% 0.19/0.40 (((~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(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(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))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(73,plain,
% 0.19/0.40 (((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[72])).
% 0.19/0.40 tff(74,plain,
% 0.19/0.40 (((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.40 tff(75,plain,
% 0.19/0.40 ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(76,plain,
% 0.19/0.40 ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.40 tff(77,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[76, 70, 44, 45, 60])).
% 0.19/0.40 tff(78,plain,((~tptp_fun__E_(s(s(s(|'0'|))), f(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(79,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[78, 43, 25])).
% 0.19/0.40 tff(80,plain,(tptp_fun__LE_(f(z), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(81,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.19/0.40 tff(82,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.19/0.40 tff(83,plain,
% 0.19/0.40 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(84,plain,
% 0.19/0.40 ($false),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[83, 7, 82])).
% 0.19/0.40 tff(85,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.40 tff(86,plain,
% 0.19/0.40 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))) <=> ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(87,plain,
% 0.19/0.40 ((tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(88,plain,
% 0.19/0.40 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (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_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[87])).
% 0.19/0.40 tff(89,plain,
% 0.19/0.41 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (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_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[88, 86])).
% 0.19/0.41 tff(90,plain,
% 0.19/0.41 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (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)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(91,plain,
% 0.19/0.41 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.41 tff(92,plain,
% 0.19/0.41 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[91, 37, 85])).
% 0.19/0.41 tff(93,plain,
% 0.19/0.41 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[92, 81])).
% 0.19/0.41 tff(94,assumption,(~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.19/0.41 tff(95,plain,
% 0.19/0.41 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(96,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[95, 7, 94])).
% 0.19/0.41 tff(97,plain,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(98,plain,
% 0.19/0.41 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))))) <=> ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(99,plain,
% 0.19/0.41 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(100,plain,
% 0.19/0.41 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.19/0.41 tff(101,plain,
% 0.19/0.41 (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[100, 20])).
% 0.19/0.41 tff(102,plain,
% 0.19/0.41 (tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[101, 97])).
% 0.19/0.41 tff(103,plain,
% 0.19/0.41 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[102, 81])).
% 0.19/0.41 tff(104,assumption,(tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))), introduced(assumption)).
% 0.19/0.41 tff(105,assumption,(tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))), introduced(assumption)).
% 0.19/0.41 tff(106,plain,
% 0.19/0.41 (((~![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(suc(z))))) | iLEQ(suc(suc(suc(z))), 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(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(107,plain,
% 0.19/0.41 ((iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (((~![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(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))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[107])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 (((~![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(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))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[108, 106])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~![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(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))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ((~![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(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.19/0.41 tff(112,plain,
% 0.19/0.41 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[111, 55, 105])).
% 0.19/0.41 tff(113,plain,
% 0.19/0.41 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[112, 104])).
% 0.19/0.41 tff(114,plain,
% 0.19/0.41 (((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(115,plain,
% 0.19/0.41 (((~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(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))))) | (~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)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(116,plain,
% 0.19/0.41 (((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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(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))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[115])).
% 0.19/0.41 tff(117,plain,
% 0.19/0.41 (((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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(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))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[116, 114])).
% 0.19/0.41 tff(118,plain,
% 0.19/0.41 ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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(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))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[119, 70, 105, 104, 113])).
% 0.19/0.42 tff(121,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,[]))).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[121, 103, 93])).
% 0.19/0.42 tff(123,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(124,assumption,(tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.19/0.42 tff(125,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), introduced(assumption)).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (^[B_41: $i] : refl((tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|)))))) <=> (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(127,plain,
% 0.19/0.42 (![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|)))))) <=> ![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.42 tff(128,plain,
% 0.19/0.42 (![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|)))))) <=> ![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(129,plain,
% 0.19/0.42 (^[B_41: $i] : rewrite((((~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_41))) | tptp_fun__LE_(f(B_41), s(s(|'0'|)))) <=> (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|)))))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(130,plain,
% 0.19/0.42 (![B_41: $i] : (((~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_41))) | tptp_fun__LE_(f(B_41), s(s(|'0'|)))) <=> ![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[129])).
% 0.19/0.42 tff(131,axiom,(![B_41: $i] : (((~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(B_41))) | tptp_fun__LE_(f(B_41), s(s(|'0'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_51')).
% 0.19/0.42 tff(132,plain,
% 0.19/0.42 (![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.42 tff(133,plain,
% 0.19/0.42 (![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.19/0.42 tff(134,plain,(
% 0.19/0.42 ![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[133])).
% 0.19/0.42 tff(135,plain,
% 0.19/0.42 (![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[134, 127])).
% 0.19/0.42 tff(136,plain,
% 0.19/0.42 (((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))) <=> ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(137,plain,
% 0.19/0.42 ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(138,plain,
% 0.19/0.42 ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.42 tff(139,plain,
% 0.19/0.42 (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'|)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[138, 135])).
% 0.19/0.42 tff(140,plain,
% 0.19/0.42 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[139, 125, 124])).
% 0.19/0.42 tff(141,assumption,(~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.19/0.42 tff(142,plain,
% 0.19/0.42 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))) <=> ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(143,plain,
% 0.19/0.42 ((tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(144,plain,
% 0.19/0.42 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (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_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[143])).
% 0.19/0.42 tff(145,plain,
% 0.19/0.42 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (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_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[144, 142])).
% 0.19/0.42 tff(146,plain,
% 0.19/0.42 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (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))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(147,plain,
% 0.19/0.42 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.19/0.42 tff(148,plain,
% 0.19/0.42 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[147, 37, 97])).
% 0.19/0.42 tff(149,plain,
% 0.19/0.42 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[148, 141])).
% 0.19/0.42 tff(150,assumption,(~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.19/0.42 tff(151,plain,
% 0.19/0.42 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(152,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[151, 7, 150])).
% 0.19/0.42 tff(153,plain,(tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))))) <=> ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|)))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(s(s(|'0'|))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[156, 20])).
% 0.19/0.43 tff(158,plain,
% 0.19/0.43 (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))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[157, 153])).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[158, 141])).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (((~![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))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(161,plain,
% 0.19/0.43 ((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))))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(162,plain,
% 0.19/0.43 (((~![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)))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[161])).
% 0.19/0.43 tff(163,plain,
% 0.19/0.43 (((~![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))))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[162, 160])).
% 0.19/0.43 tff(164,plain,
% 0.19/0.43 ((~![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)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(165,plain,
% 0.19/0.43 ((~![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)))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.19/0.43 tff(166,plain,
% 0.19/0.43 ((~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)))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[165, 55])).
% 0.19/0.43 tff(167,plain,
% 0.19/0.43 (iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[166, 159, 149])).
% 0.19/0.43 tff(168,plain,
% 0.19/0.43 (((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | (~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)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(169,plain,
% 0.19/0.43 (((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(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)))))) | (~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))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(170,plain,
% 0.19/0.43 (((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(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)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))) <=> ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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))))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[169])).
% 0.19/0.43 tff(171,plain,
% 0.19/0.43 (((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(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)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))) <=> ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | (~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)))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[170, 168])).
% 0.19/0.43 tff(172,plain,
% 0.19/0.43 ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(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)))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z)))))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(173,plain,
% 0.19/0.43 ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(suc(z)))), suc(suc(suc(suc(z))))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.43 tff(174,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[173, 70, 149, 159, 167])).
% 0.19/0.43 tff(175,plain,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(176,plain,
% 0.19/0.43 (^[B_41: $i] : refl((tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|)))))) <=> (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(177,plain,
% 0.19/0.43 (![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|)))))) <=> ![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[176])).
% 0.19/0.43 tff(178,plain,
% 0.19/0.43 (![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|)))))) <=> ![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(179,plain,
% 0.19/0.43 (^[B_41: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41)))) | tptp_fun__LE_(f(B_41), s(s(|'0'|)))) <=> (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(180,plain,
% 0.19/0.43 (![B_41: $i] : (((~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41)))) | tptp_fun__LE_(f(B_41), s(s(|'0'|)))) <=> ![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[179])).
% 0.19/0.43 tff(181,axiom,(![B_41: $i] : (((~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41)))) | tptp_fun__LE_(f(B_41), s(s(|'0'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_84')).
% 0.19/0.44 tff(182,plain,
% 0.19/0.44 (![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.19/0.44 tff(183,plain,
% 0.19/0.44 (![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[182, 178])).
% 0.19/0.44 tff(184,plain,(
% 0.19/0.44 ![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[183])).
% 0.19/0.44 tff(185,plain,
% 0.19/0.44 (![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[184, 177])).
% 0.19/0.44 tff(186,plain,
% 0.19/0.44 (((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), 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_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), 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'|))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(187,plain,
% 0.19/0.44 ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), 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'|))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(188,plain,
% 0.19/0.44 ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), 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'|)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.19/0.44 tff(189,plain,
% 0.19/0.44 (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'|)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[188, 185])).
% 0.19/0.44 tff(190,plain,
% 0.19/0.44 (tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[189, 125, 175])).
% 0.19/0.44 tff(191,assumption,(tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))), introduced(assumption)).
% 0.19/0.44 tff(192,assumption,(tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))), introduced(assumption)).
% 0.19/0.44 tff(193,plain,
% 0.19/0.44 (^[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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(194,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[193])).
% 0.19/0.44 tff(195,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(196,plain,
% 0.19/0.44 (^[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)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(197,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[196])).
% 0.19/0.44 tff(198,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/sandbox2/benchmark/theBenchmark.p','clause_5')).
% 0.19/0.44 tff(199,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.19/0.44 tff(200,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[199, 195])).
% 0.19/0.44 tff(201,plain,(
% 0.19/0.44 ![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))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[200])).
% 0.19/0.44 tff(202,plain,
% 0.19/0.44 (![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))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[201, 194])).
% 0.19/0.44 tff(203,plain,
% 0.19/0.44 (((~![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)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(204,plain,
% 0.19/0.44 ((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)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(205,plain,
% 0.19/0.44 (((~![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))))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[204])).
% 0.19/0.44 tff(206,plain,
% 0.19/0.44 (((~![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)))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[205, 203])).
% 0.19/0.44 tff(207,plain,
% 0.19/0.44 ((~![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))))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(208,plain,
% 0.19/0.44 ((~![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))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.44 tff(209,plain,
% 0.19/0.44 ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[208, 202])).
% 0.19/0.44 tff(210,plain,
% 0.19/0.44 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[209, 192, 191])).
% 0.19/0.44 tff(211,plain,
% 0.19/0.44 (^[B_43: $i, B_42: $i, A_2: $i] : refl(((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) <=> ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(212,plain,
% 0.19/0.44 (![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) <=> ![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[211])).
% 0.19/0.44 tff(213,plain,
% 0.19/0.44 (![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) <=> ![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(214,plain,
% 0.19/0.44 (^[B_43: $i, B_42: $i, A_2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))), ((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) | (~iLEQ(suc(B_42), suc(B_43)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) | (~iLEQ(suc(B_42), suc(B_43)))) <=> ((~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))), ((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) <=> ((~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))))), (((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) <=> (((~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))))), rewrite((((~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))), (((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))))), ((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43))))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43))))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))), ((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))))), (((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43))))) | (~iLEQ(suc(A_2), suc(B_42)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) | (~iLEQ(suc(A_2), suc(B_42)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) | (~iLEQ(suc(A_2), suc(B_42)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))), (((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43))))) | (~iLEQ(suc(A_2), suc(B_42)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))))), ((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43))))) | (~iLEQ(suc(A_2), suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))), ((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43))))) | (~iLEQ(suc(A_2), suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43)))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))))), (((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43))))) | (~iLEQ(suc(A_2), suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> (((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))))), rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42))))) | (~tptp_fun__E_(s(s(|'0'|)), f(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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))), (((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43))))) | (~iLEQ(suc(A_2), suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(215,plain,
% 0.19/0.45 (![B_43: $i, B_42: $i, A_2: $i] : ((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43))))) | (~iLEQ(suc(A_2), suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2)))) <=> ![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[214])).
% 0.19/0.45 tff(216,axiom,(![B_43: $i, B_42: $i, A_2: $i] : ((((((((~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42)))) | (~iLEQ(suc(B_42), suc(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43))))) | (~iLEQ(suc(A_2), suc(B_42)))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_20')).
% 0.19/0.45 tff(217,plain,
% 0.19/0.45 (![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.19/0.45 tff(218,plain,
% 0.19/0.45 (![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[217, 213])).
% 0.19/0.45 tff(219,plain,(
% 0.19/0.45 ![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[218])).
% 0.19/0.45 tff(220,plain,
% 0.19/0.45 (![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[219, 212])).
% 0.19/0.45 tff(221,plain,
% 0.19/0.45 (((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~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_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(222,plain,
% 0.19/0.45 (((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~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))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(223,plain,
% 0.19/0.45 (((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~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_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[222])).
% 0.19/0.45 tff(224,plain,
% 0.19/0.45 (((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~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_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[223, 221])).
% 0.19/0.45 tff(225,plain,
% 0.19/0.45 ((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~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)))))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(226,plain,
% 0.19/0.45 ((~![B_43: $i, B_42: $i, A_2: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.19/0.45 tff(227,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[226, 220, 191, 192, 210])).
% 0.19/0.45 tff(228,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,[]))).
% 0.19/0.45 tff(229,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[228, 190, 140])).
% 0.19/0.45 tff(230,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(231,plain,
% 0.19/0.46 (tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[230, 123])).
% 0.19/0.46 tff(232,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))), introduced(assumption)).
% 0.19/0.46 tff(233,plain,
% 0.19/0.46 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))))) <=> ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(234,plain,
% 0.19/0.46 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|)))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(235,plain,
% 0.19/0.46 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_23))) | (~tptp_fun__LE_(f(suc(B_23)), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(s(|'0'|))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.19/0.46 tff(236,plain,
% 0.19/0.46 (tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[235, 20, 85])).
% 0.19/0.46 tff(237,plain,
% 0.19/0.46 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[236, 232])).
% 0.19/0.46 tff(238,plain,
% 0.19/0.46 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))) <=> ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(239,plain,
% 0.19/0.46 ((tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(240,plain,
% 0.19/0.46 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (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_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[239])).
% 0.19/0.46 tff(241,plain,
% 0.19/0.46 (((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (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_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[240, 238])).
% 0.19/0.46 tff(242,plain,
% 0.19/0.46 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | (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))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(243,plain,
% 0.19/0.46 ((~![B_23: $i] : (tptp_fun__LE_(f(B_23), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(B_23), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_23)))) | tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.19/0.46 tff(244,plain,
% 0.19/0.46 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[243, 37])).
% 0.19/0.46 tff(245,plain,
% 0.19/0.46 (tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[244, 232, 9])).
% 0.19/0.46 tff(246,plain,
% 0.19/0.46 (((~![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))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(247,plain,
% 0.19/0.46 ((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(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))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(248,plain,
% 0.19/0.46 (((~![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)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[247])).
% 0.19/0.46 tff(249,plain,
% 0.19/0.46 (((~![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))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[248, 246])).
% 0.19/0.46 tff(250,plain,
% 0.19/0.46 ((~![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)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(251,plain,
% 0.19/0.46 ((~![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)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.19/0.46 tff(252,plain,
% 0.19/0.46 (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[251, 55, 44])).
% 0.19/0.46 tff(253,plain,
% 0.19/0.46 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[252, 105])).
% 0.19/0.46 tff(254,plain,
% 0.19/0.46 (((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | (~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)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(255,plain,
% 0.19/0.46 (((~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(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)))) | (~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))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(256,plain,
% 0.19/0.46 (((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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(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)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[255])).
% 0.19/0.46 tff(257,plain,
% 0.19/0.46 (((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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(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)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | (~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)))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[256, 254])).
% 0.19/0.46 tff(258,plain,
% 0.19/0.46 ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | ((~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(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)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(259,plain,
% 0.19/0.46 ((~![B_25: $i, A_1: $i, B_24: $i] : ((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(A_1)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_25)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(B_24)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_1))) | (~iLEQ(suc(A_1), suc(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_24))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(B_25))) | (~iLEQ(suc(B_24), suc(B_25))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.19/0.46 tff(260,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[259, 70, 44, 105, 253])).
% 0.19/0.46 tff(261,plain,((~tptp_fun__E_(s(s(s(|'0'|))), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(262,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[261, 245, 237])).
% 0.19/0.46 tff(263,plain,(tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(264,assumption,(~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))), introduced(assumption)).
% 0.19/0.46 tff(265,assumption,(~tptp_fun__LE_(f(z), s(|'0'|))), introduced(assumption)).
% 0.19/0.46 tff(266,assumption,(tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))), introduced(assumption)).
% 0.19/0.46 tff(267,plain,
% 0.19/0.46 (((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))) <=> ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(268,plain,
% 0.19/0.46 ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(269,plain,
% 0.19/0.46 ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.19/0.46 tff(270,plain,
% 0.19/0.46 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[269, 135])).
% 0.19/0.46 tff(271,plain,
% 0.19/0.46 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[270, 264, 266])).
% 0.19/0.46 tff(272,plain,
% 0.19/0.46 (^[B_53: $i] : refl((tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(273,plain,
% 0.19/0.46 (![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|))))) <=> ![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[272])).
% 0.19/0.46 tff(274,plain,
% 0.19/0.46 (![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|))))) <=> ![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(275,plain,
% 0.19/0.46 (^[B_53: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_53)))) | tptp_fun__LE_(f(B_53), s(|'0'|))) <=> (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(276,plain,
% 0.19/0.46 (![B_53: $i] : (((~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_53)))) | tptp_fun__LE_(f(B_53), s(|'0'|))) <=> ![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[275])).
% 0.19/0.46 tff(277,axiom,(![B_53: $i] : (((~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_53)))) | tptp_fun__LE_(f(B_53), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_15')).
% 0.19/0.46 tff(278,plain,
% 0.19/0.46 (![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.19/0.46 tff(279,plain,
% 0.19/0.46 (![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[278, 274])).
% 0.19/0.46 tff(280,plain,(
% 0.19/0.46 ![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[279])).
% 0.19/0.46 tff(281,plain,
% 0.19/0.46 (![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[280, 273])).
% 0.19/0.46 tff(282,plain,
% 0.19/0.46 (((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), 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_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), 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'|)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(283,plain,
% 0.19/0.46 ((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), 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'|)))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(284,plain,
% 0.19/0.46 ((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), 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'|))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.19/0.46 tff(285,plain,
% 0.19/0.46 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[284, 281])).
% 0.19/0.46 tff(286,plain,
% 0.19/0.46 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[285, 271, 265])).
% 0.19/0.47 tff(287,plain,
% 0.19/0.47 (((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), 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_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(288,plain,
% 0.19/0.47 ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(289,plain,
% 0.19/0.47 ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[288, 287])).
% 0.19/0.47 tff(290,plain,
% 0.19/0.47 (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[289, 185])).
% 0.19/0.47 tff(291,plain,
% 0.19/0.47 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[290, 264, 266])).
% 0.19/0.47 tff(292,plain,
% 0.19/0.47 (^[B_53: $i] : refl((tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(293,plain,
% 0.19/0.47 (![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|))))) <=> ![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[292])).
% 0.19/0.47 tff(294,plain,
% 0.19/0.47 (![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|))))) <=> ![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(295,plain,
% 0.19/0.47 (^[B_53: $i] : rewrite((((~tptp_fun__LE_(f(B_53), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_53))) | tptp_fun__LE_(f(B_53), s(|'0'|))) <=> (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(296,plain,
% 0.19/0.47 (![B_53: $i] : (((~tptp_fun__LE_(f(B_53), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_53))) | tptp_fun__LE_(f(B_53), s(|'0'|))) <=> ![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[295])).
% 0.19/0.47 tff(297,axiom,(![B_53: $i] : (((~tptp_fun__LE_(f(B_53), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_53))) | tptp_fun__LE_(f(B_53), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_6')).
% 0.19/0.47 tff(298,plain,
% 0.19/0.47 (![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.19/0.47 tff(299,plain,
% 0.19/0.47 (![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[298, 294])).
% 0.19/0.47 tff(300,plain,(
% 0.19/0.47 ![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[299])).
% 0.19/0.47 tff(301,plain,
% 0.19/0.47 (![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[300, 293])).
% 0.19/0.47 tff(302,plain,
% 0.19/0.47 (((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), 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_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(303,plain,
% 0.19/0.47 ((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(304,plain,
% 0.19/0.47 ((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.19/0.47 tff(305,plain,
% 0.19/0.47 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z)) | (~tptp_fun__LE_(f(z), s(s(|'0'|))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[304, 301])).
% 0.19/0.47 tff(306,plain,
% 0.19/0.47 (tptp_fun__E_(s(|'0'|), f(z))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[305, 291, 265])).
% 0.19/0.47 tff(307,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(308,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[307])).
% 0.19/0.47 tff(309,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(310,plain,
% 0.19/0.47 (^[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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(311,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[310])).
% 0.19/0.47 tff(312,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/sandbox2/benchmark/theBenchmark.p','clause_91')).
% 0.19/0.47 tff(313,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.19/0.47 tff(314,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[313, 309])).
% 0.19/0.47 tff(315,plain,(
% 0.19/0.47 ![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))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[314])).
% 0.19/0.47 tff(316,plain,
% 0.19/0.47 (![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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[315, 308])).
% 0.19/0.47 tff(317,plain,
% 0.19/0.47 (((~![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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(318,plain,
% 0.19/0.47 ((~![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))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(319,plain,
% 0.19/0.47 ((~![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)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.19/0.47 tff(320,plain,
% 0.19/0.47 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[319, 316])).
% 0.19/0.47 tff(321,plain,
% 0.19/0.47 (iLEQ(suc(z), suc(z))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[320, 306, 286])).
% 0.19/0.47 tff(322,plain,
% 0.19/0.47 (^[B_55: $i, A_3: $i, B_54: $i] : refl(((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(323,plain,
% 0.19/0.47 (![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) <=> ![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[322])).
% 0.19/0.47 tff(324,plain,
% 0.19/0.47 (![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) <=> ![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(325,plain,
% 0.19/0.47 (^[B_55: $i, A_3: $i, B_54: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) <=> ((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))), (((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) <=> (((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))))), rewrite((((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) <=> ((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))), (((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) <=> ((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))))), ((((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> (((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))))), rewrite((((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> ((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))), ((((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) <=> ((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))))), (((((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_55)))) <=> (((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_55)))))), rewrite((((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_55)))) <=> ((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))), (((((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_55)))) <=> ((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))))), ((((((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_54))))) <=> (((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_54))))))), rewrite((((~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_54))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))), ((((((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_54))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))))), (((((((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_54))))) | (~tptp_fun__E_(s(|'0'|), f(B_54)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_54)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_54)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))), (((((((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_54))))) | (~tptp_fun__E_(s(|'0'|), f(B_54)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(326,plain,
% 0.19/0.47 (![B_55: $i, A_3: $i, B_54: $i] : ((((((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_54))))) | (~tptp_fun__E_(s(|'0'|), f(B_54)))) <=> ![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[325])).
% 0.19/0.47 tff(327,axiom,(![B_55: $i, A_3: $i, B_54: $i] : ((((((((~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3))))) | (~iLEQ(suc(A_3), suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55))))) | (~tptp_fun__E_(s(|'0'|), f(A_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_54))))) | (~tptp_fun__E_(s(|'0'|), f(B_54))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_21')).
% 0.19/0.47 tff(328,plain,
% 0.19/0.47 (![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.19/0.47 tff(329,plain,
% 0.19/0.47 (![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[328, 324])).
% 0.19/0.47 tff(330,plain,(
% 0.19/0.47 ![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[329])).
% 0.19/0.47 tff(331,plain,
% 0.19/0.47 (![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[330, 323])).
% 0.19/0.47 tff(332,plain,
% 0.19/0.47 (((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(333,plain,
% 0.19/0.47 (((~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))) | (~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(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(334,plain,
% 0.19/0.47 (((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | ((~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))) | (~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)))))) <=> ((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[333])).
% 0.19/0.47 tff(335,plain,
% 0.19/0.47 (((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | ((~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))) | (~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)))))) <=> ((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[334, 332])).
% 0.19/0.48 tff(336,plain,
% 0.19/0.48 ((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | ((~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))) | (~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)))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(337,plain,
% 0.19/0.48 ((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.19/0.48 tff(338,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[337, 331, 286, 306, 321])).
% 0.19/0.48 tff(339,plain,(tptp_fun__E_(s(s(|'0'|)), f(suc(z))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.48 tff(340,plain,
% 0.19/0.48 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[339, 264, 263])).
% 0.19/0.48 tff(341,plain,
% 0.19/0.48 (^[B_60: $i] : refl((tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|)))) <=> (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(342,plain,
% 0.19/0.48 (![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|)))) <=> ![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[341])).
% 0.19/0.48 tff(343,plain,
% 0.19/0.48 (![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|)))) <=> ![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(344,plain,
% 0.19/0.48 (^[B_60: $i] : rewrite((((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_60))) | tptp_fun__LE_(f(B_60), |'0'|)) <=> (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(345,plain,
% 0.19/0.48 (![B_60: $i] : (((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_60))) | tptp_fun__LE_(f(B_60), |'0'|)) <=> ![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[344])).
% 0.19/0.48 tff(346,axiom,(![B_60: $i] : (((~tptp_fun__LE_(f(B_60), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_60))) | tptp_fun__LE_(f(B_60), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_96')).
% 0.19/0.48 tff(347,plain,
% 0.19/0.48 (![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.19/0.48 tff(348,plain,
% 0.19/0.48 (![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[347, 343])).
% 0.19/0.48 tff(349,plain,(
% 0.19/0.48 ![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[348])).
% 0.19/0.48 tff(350,plain,
% 0.19/0.48 (![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[349, 342])).
% 0.19/0.48 tff(351,plain,
% 0.19/0.48 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(352,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_66')).
% 0.19/0.48 tff(353,plain,
% 0.19/0.48 (~tptp_fun__LE_(f(z), |'0'|)),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.19/0.48 tff(354,plain,
% 0.19/0.48 (((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(355,plain,
% 0.19/0.48 ((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'|))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(356,plain,
% 0.19/0.48 (((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[355])).
% 0.19/0.48 tff(357,plain,
% 0.19/0.48 (((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[356, 354])).
% 0.19/0.48 tff(358,plain,
% 0.19/0.48 ((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(359,plain,
% 0.19/0.48 ((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(B_60)) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(B_60), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.19/0.48 tff(360,plain,
% 0.19/0.48 (tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[359, 353, 350])).
% 0.19/0.48 tff(361,plain,
% 0.19/0.48 (tptp_fun__E_(|'0'|, f(z))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[360, 340])).
% 0.19/0.48 tff(362,assumption,(tptp_fun__E_(|'0'|, f(z))), introduced(assumption)).
% 0.19/0.48 tff(363,assumption,(tptp_fun__E_(|'0'|, f(suc(z)))), introduced(assumption)).
% 0.19/0.48 tff(364,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(365,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[364])).
% 0.19/0.48 tff(366,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(367,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(368,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[367])).
% 0.19/0.48 tff(369,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/sandbox2/benchmark/theBenchmark.p','clause_109')).
% 0.19/0.48 tff(370,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.19/0.48 tff(371,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[370, 366])).
% 0.19/0.48 tff(372,plain,(
% 0.19/0.48 ![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))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[371])).
% 0.19/0.48 tff(373,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[372, 365])).
% 0.19/0.48 tff(374,plain,
% 0.19/0.48 (((~![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(375,plain,
% 0.19/0.48 ((~![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))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(376,plain,
% 0.19/0.48 ((~![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)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.19/0.48 tff(377,plain,
% 0.19/0.48 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[376, 373])).
% 0.19/0.48 tff(378,plain,
% 0.19/0.48 (iLEQ(suc(z), suc(z))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[377, 363, 362])).
% 0.19/0.48 tff(379,plain,
% 0.19/0.48 (^[A_4: $i, B_62: $i, B_61: $i] : refl(((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(380,plain,
% 0.19/0.48 (![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) <=> ![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[379])).
% 0.19/0.48 tff(381,plain,
% 0.19/0.48 (![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) <=> ![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(382,plain,
% 0.19/0.48 (^[A_4: $i, B_62: $i, B_61: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_4), suc(B_61))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_4), suc(B_61)))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~tptp_fun__E_(|'0'|, f(B_62)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_62)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_62)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~tptp_fun__E_(|'0'|, f(B_62)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~tptp_fun__E_(|'0'|, f(B_62)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(A_4)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~tptp_fun__E_(|'0'|, f(B_62)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(383,plain,
% 0.19/0.48 (![A_4: $i, B_62: $i, B_61: $i] : ((((((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~tptp_fun__E_(|'0'|, f(B_62)))) | (~tptp_fun__E_(|'0'|, f(A_4)))) <=> ![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[382])).
% 0.19/0.48 tff(384,axiom,(![A_4: $i, B_62: $i, B_61: $i] : ((((((((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~iLEQ(suc(B_61), suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62))))) | (~tptp_fun__E_(|'0'|, f(B_61)))) | (~tptp_fun__E_(|'0'|, f(suc(A_4))))) | (~tptp_fun__E_(|'0'|, f(B_62)))) | (~tptp_fun__E_(|'0'|, f(A_4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_144')).
% 0.19/0.48 tff(385,plain,
% 0.19/0.48 (![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.19/0.48 tff(386,plain,
% 0.19/0.48 (![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[385, 381])).
% 0.19/0.48 tff(387,plain,(
% 0.19/0.48 ![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[386])).
% 0.19/0.48 tff(388,plain,
% 0.19/0.48 (![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[387, 380])).
% 0.19/0.48 tff(389,plain,
% 0.19/0.48 (((~![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(390,plain,
% 0.19/0.49 (((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(391,plain,
% 0.19/0.49 (((~![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[390])).
% 0.19/0.49 tff(392,plain,
% 0.19/0.49 (((~![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[391, 389])).
% 0.19/0.49 tff(393,plain,
% 0.19/0.49 ((~![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(394,plain,
% 0.19/0.49 ((~![A_4: $i, B_62: $i, B_61: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_61)))) | (~tptp_fun__E_(|'0'|, f(B_61))) | (~iLEQ(suc(B_61), suc(B_62))) | (~tptp_fun__E_(|'0'|, f(A_4))) | (~tptp_fun__E_(|'0'|, f(B_62))) | (~tptp_fun__E_(|'0'|, f(suc(A_4)))) | (~tptp_fun__E_(|'0'|, f(suc(B_62)))) | (~iLEQ(suc(A_4), suc(B_61))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.19/0.49 tff(395,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[394, 388, 362, 363, 378])).
% 0.19/0.49 tff(396,plain,((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(397,plain,
% 0.19/0.49 (~tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[396, 361])).
% 0.19/0.49 tff(398,plain,
% 0.19/0.49 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[339, 266, 264])).
% 0.19/0.49 tff(399,plain,
% 0.19/0.49 (tptp_fun__E_(|'0'|, f(z))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[360, 398])).
% 0.19/0.49 tff(400,assumption,(~tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 0.19/0.49 tff(401,plain,
% 0.19/0.49 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | (~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[269, 135, 264])).
% 0.19/0.49 tff(402,plain,
% 0.19/0.49 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[401, 266])).
% 0.19/0.49 tff(403,plain,
% 0.19/0.49 (((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), 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_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), 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'|)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(404,plain,
% 0.19/0.49 ((tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))) <=> (tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(405,plain,
% 0.19/0.49 (((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), 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'|))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[404])).
% 0.19/0.49 tff(406,plain,
% 0.19/0.49 (((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))) <=> ((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), 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'|)))),
% 0.19/0.49 inference(transitivity,[status(thm)],[405, 403])).
% 0.19/0.49 tff(407,plain,
% 0.19/0.49 ((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(408,plain,
% 0.19/0.49 ((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_53)) | (~tptp_fun__LE_(f(B_53), 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'|))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.19/0.49 tff(409,plain,
% 0.19/0.49 (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'|))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[408, 301])).
% 0.19/0.49 tff(410,plain,
% 0.19/0.49 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[409, 402, 400])).
% 0.19/0.49 tff(411,plain,
% 0.19/0.49 (^[B_60: $i] : refl((tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|)))) <=> (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(412,plain,
% 0.19/0.49 (![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|)))) <=> ![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[411])).
% 0.19/0.49 tff(413,plain,
% 0.19/0.49 (![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|)))) <=> ![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(414,plain,
% 0.19/0.49 (^[B_60: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) | tptp_fun__LE_(f(B_60), |'0'|)) <=> (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(415,plain,
% 0.19/0.49 (![B_60: $i] : (((~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) | tptp_fun__LE_(f(B_60), |'0'|)) <=> ![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[414])).
% 0.19/0.49 tff(416,axiom,(![B_60: $i] : (((~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_60)))) | tptp_fun__LE_(f(B_60), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_114')).
% 0.19/0.49 tff(417,plain,
% 0.19/0.49 (![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[416, 415])).
% 0.19/0.49 tff(418,plain,
% 0.19/0.49 (![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[417, 413])).
% 0.19/0.49 tff(419,plain,(
% 0.19/0.49 ![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[418])).
% 0.19/0.49 tff(420,plain,
% 0.19/0.49 (![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[419, 412])).
% 0.19/0.49 tff(421,plain,
% 0.19/0.49 (((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))) <=> ((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(422,plain,
% 0.19/0.49 ((tptp_fun__E_(|'0'|, f(suc(z))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))) <=> (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(423,plain,
% 0.19/0.49 (((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(suc(z))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))) <=> ((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[422])).
% 0.19/0.49 tff(424,plain,
% 0.19/0.49 (((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(suc(z))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))) <=> ((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[423, 421])).
% 0.19/0.49 tff(425,plain,
% 0.19/0.49 ((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(suc(z))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(426,plain,
% 0.19/0.49 ((~![B_60: $i] : (tptp_fun__E_(|'0'|, f(suc(B_60))) | tptp_fun__LE_(f(B_60), |'0'|) | (~tptp_fun__LE_(f(suc(B_60)), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[425, 424])).
% 0.19/0.49 tff(427,plain,
% 0.19/0.49 (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[426, 420, 353])).
% 0.19/0.49 tff(428,plain,
% 0.19/0.49 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[427, 410])).
% 0.19/0.49 tff(429,plain,
% 0.19/0.49 (iLEQ(suc(z), suc(z))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[377, 428, 399])).
% 0.19/0.49 tff(430,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[394, 388, 399, 428, 429])).
% 0.19/0.49 tff(431,plain,((~tptp_fun__LE_(f(suc(z)), s(s(s(|'0'|))))) | tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__E_(s(s(|'0'|)), f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(432,plain,
% 0.19/0.49 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[431, 264, 263])).
% 0.19/0.49 tff(433,assumption,(tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 0.19/0.49 tff(434,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 0.19/0.49 tff(435,plain,
% 0.19/0.49 (((~![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))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(436,plain,
% 0.19/0.49 ((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))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(437,plain,
% 0.19/0.49 (((~![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)))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[436])).
% 0.19/0.49 tff(438,plain,
% 0.19/0.49 (((~![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))))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[437, 435])).
% 0.19/0.49 tff(439,plain,
% 0.19/0.49 ((~![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)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(440,plain,
% 0.19/0.49 ((~![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)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.19/0.49 tff(441,plain,
% 0.19/0.49 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[440, 316])).
% 0.19/0.49 tff(442,plain,
% 0.19/0.49 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[441, 434, 433])).
% 0.19/0.49 tff(443,plain,
% 0.19/0.49 (((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | ((~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_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(444,plain,
% 0.19/0.49 (((~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)))) | (~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))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(445,plain,
% 0.19/0.49 (((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | ((~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)))) | (~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))))))) <=> ((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[444])).
% 0.19/0.49 tff(446,plain,
% 0.19/0.49 (((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | ((~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)))) | (~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))))))) <=> ((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[445, 443])).
% 0.19/0.49 tff(447,plain,
% 0.19/0.49 ((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | ((~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)))) | (~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))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(448,plain,
% 0.19/0.49 ((~![B_55: $i, A_3: $i, B_54: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_54)))) | (~tptp_fun__E_(s(|'0'|), f(B_54))) | (~iLEQ(suc(A_3), suc(B_54))) | (~iLEQ(suc(B_54), suc(B_55))) | (~tptp_fun__E_(s(|'0'|), f(B_55))) | (~tptp_fun__E_(s(|'0'|), f(A_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_55)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.19/0.49 tff(449,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[448, 331, 433, 434, 442])).
% 0.19/0.49 tff(450,plain,((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(451,plain,
% 0.19/0.49 (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[450, 432])).
% 0.19/0.49 tff(452,plain,
% 0.19/0.49 (((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), 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_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(453,plain,
% 0.19/0.49 ((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(454,plain,
% 0.19/0.49 ((~![B_53: $i] : (tptp_fun__LE_(f(B_53), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_53))) | (~tptp_fun__LE_(f(suc(B_53)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.19/0.49 tff(455,plain,
% 0.19/0.49 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[454, 281])).
% 0.19/0.49 tff(456,plain,
% 0.19/0.49 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[455, 451, 231])).
% 0.19/0.49 tff(457,plain,
% 0.19/0.49 ($false),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[427, 456, 397])).
% 0.19/0.49 tff(458,plain,(tptp_fun__E_(s(s(|'0'|)), f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.49 tff(459,assumption,(tptp_fun__E_(s(s(|'0'|)), f(suc(z)))), introduced(assumption)).
% 0.19/0.49 tff(460,plain,
% 0.19/0.49 (((~![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))))) | ((~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))))) <=> ((~![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(z)))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(461,plain,
% 0.19/0.50 ((iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(462,plain,
% 0.19/0.50 (((~![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(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[461])).
% 0.19/0.50 tff(463,plain,
% 0.19/0.50 (((~![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(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[462, 460])).
% 0.19/0.50 tff(464,plain,
% 0.19/0.50 ((~![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)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(465,plain,
% 0.19/0.50 ((~![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(z)))) | iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.19/0.50 tff(466,plain,
% 0.19/0.50 ((~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)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[465, 202])).
% 0.19/0.50 tff(467,plain,
% 0.19/0.50 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[466, 191, 459])).
% 0.19/0.50 tff(468,plain,
% 0.19/0.50 (((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~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)))))) <=> ((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | (~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)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(469,plain,
% 0.19/0.50 (((~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))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(470,plain,
% 0.19/0.50 (((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~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))))) | (~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_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~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))))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[469])).
% 0.19/0.50 tff(471,plain,
% 0.19/0.50 (((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~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))))) | (~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_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | (~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)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[470, 468])).
% 0.19/0.50 tff(472,plain,
% 0.19/0.50 ((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~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))))) | (~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))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(473,plain,
% 0.19/0.50 ((~![B_43: $i, B_42: $i, A_2: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[472, 471])).
% 0.19/0.50 tff(474,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[473, 220, 459, 191, 467])).
% 0.19/0.50 tff(475,plain,((~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(476,plain,
% 0.19/0.50 (~tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[475, 458])).
% 0.19/0.50 tff(477,plain,
% 0.19/0.50 (((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), 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_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(478,plain,
% 0.19/0.50 ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(479,plain,
% 0.19/0.50 ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(B_41))) | (~tptp_fun__LE_(f(suc(B_41)), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[478, 477])).
% 0.19/0.50 tff(480,plain,
% 0.19/0.50 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(s(|'0'|)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[479, 185])).
% 0.19/0.50 tff(481,plain,
% 0.19/0.50 (tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[480, 476, 123])).
% 0.19/0.50 tff(482,plain,
% 0.19/0.50 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[409, 400, 481])).
% 0.19/0.50 tff(483,plain,
% 0.19/0.50 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[427, 482])).
% 0.19/0.50 tff(484,plain,
% 0.19/0.50 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[285, 400, 481])).
% 0.19/0.50 tff(485,plain,
% 0.19/0.50 (tptp_fun__E_(|'0'|, f(z))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[360, 484])).
% 0.19/0.50 tff(486,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[396, 485, 483])).
% 0.19/0.50 tff(487,plain,(tptp_fun__E_(s(|'0'|), f(suc(z)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(488,plain,
% 0.19/0.50 (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[450, 487])).
% 0.19/0.50 tff(489,plain,
% 0.19/0.50 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[455, 488, 231])).
% 0.19/0.50 tff(490,plain,
% 0.19/0.50 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[427, 489])).
% 0.19/0.50 tff(491,plain,
% 0.19/0.50 (~tptp_fun__E_(|'0'|, f(z))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[396, 490])).
% 0.19/0.50 tff(492,plain,
% 0.19/0.50 (~tptp_fun__LE_(f(z), s(|'0'|))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[360, 491])).
% 0.19/0.50 tff(493,assumption,(~iLEQ(suc(z), suc(z))), introduced(assumption)).
% 0.19/0.50 tff(494,plain,
% 0.19/0.50 (~tptp_fun__E_(s(|'0'|), f(z))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[320, 493, 487])).
% 0.19/0.50 tff(495,plain,
% 0.19/0.50 (((~![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))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(496,plain,
% 0.19/0.50 ((~![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))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(497,plain,
% 0.19/0.50 ((~![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)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[496, 495])).
% 0.19/0.50 tff(498,plain,
% 0.19/0.50 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[497, 202])).
% 0.19/0.50 tff(499,plain,
% 0.19/0.50 (~tptp_fun__E_(s(s(|'0'|)), f(z))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[498, 493, 458])).
% 0.19/0.50 tff(500,plain,
% 0.19/0.50 (((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))))) <=> ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(501,plain,
% 0.19/0.50 ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|))))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(502,plain,
% 0.19/0.50 ((~![B_41: $i] : (tptp_fun__LE_(f(B_41), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_41)) | (~tptp_fun__LE_(f(B_41), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.19/0.50 tff(503,plain,
% 0.19/0.50 (tptp_fun__LE_(f(z), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(z)) | (~tptp_fun__LE_(f(z), s(s(s(|'0'|)))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[502, 135])).
% 0.19/0.50 tff(504,plain,
% 0.19/0.50 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[503, 499, 80])).
% 0.19/0.50 tff(505,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[305, 504, 494, 492])).
% 0.19/0.50 tff(506,plain,(iLEQ(suc(z), suc(z))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(507,plain,
% 0.19/0.50 (((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(508,plain,
% 0.19/0.50 (((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~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))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(509,plain,
% 0.19/0.50 (((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~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_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[508])).
% 0.19/0.51 tff(510,plain,
% 0.19/0.51 (((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~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_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[509, 507])).
% 0.19/0.51 tff(511,plain,
% 0.19/0.51 ((~![B_43: $i, B_42: $i, A_2: $i] : ((~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(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~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)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(512,plain,
% 0.19/0.51 ((~![B_43: $i, B_42: $i, A_2: $i] : ((~tptp_fun__E_(s(s(|'0'|)), f(suc(A_2)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_2))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_43))) | (~iLEQ(suc(A_2), suc(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_43)))) | (~iLEQ(suc(B_42), suc(B_43))) | (~tptp_fun__E_(s(s(|'0'|)), f(B_42))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(B_42)))))) | (~tptp_fun__E_(s(s(|'0'|)), f(suc(z)))) | (~tptp_fun__E_(s(s(|'0'|)), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.19/0.51 tff(513,plain,
% 0.19/0.51 (~tptp_fun__E_(s(s(|'0'|)), f(z))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[512, 220, 458, 506])).
% 0.19/0.51 tff(514,plain,
% 0.19/0.51 (~tptp_fun__E_(s(|'0'|), f(z))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[337, 331, 487, 506])).
% 0.19/0.51 tff(515,plain,
% 0.19/0.51 (~tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[305, 514, 492])).
% 0.19/0.51 tff(516,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[503, 515, 513, 80])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------