%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO657-1 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:42:02 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO657-1 : TPTP v9.0.0. Released v7.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 13:21:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 tff(tptp_fun__E__type, type, (
% 0.18/0.38 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.18/0.38 tff(f_type, type, (
% 0.18/0.38 f: $i > $i)).
% 0.18/0.38 tff(suc_type, type, (
% 0.18/0.38 suc: $i > $i)).
% 0.18/0.38 tff(z_type, type, (
% 0.18/0.38 z: $i)).
% 0.18/0.38 tff(tptp_fun__0__type, type, (
% 0.18/0.38 tptp_fun__0_: $i)).
% 0.18/0.38 tff(tptp_fun__LE__type, type, (
% 0.18/0.38 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.18/0.38 tff(s_type, type, (
% 0.18/0.38 s: $i > $i)).
% 0.18/0.38 tff(iLEQ_type, type, (
% 0.18/0.38 iLEQ: ( $i * $i ) > $o)).
% 0.18/0.38 tff(1,assumption,(~tptp_fun__LE_(f(suc(z)), s(|'0'|))), introduced(assumption)).
% 0.18/0.38 tff(2,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 0.18/0.38 tff(3,plain,
% 0.18/0.38 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(s(|'0'|))) <=> tptp_fun__LE_(f(A), s(s(|'0'|))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(4,plain,
% 0.18/0.38 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.38 tff(5,plain,
% 0.18/0.38 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(6,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_17')).
% 0.18/0.38 tff(7,plain,
% 0.18/0.38 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.38 tff(8,plain,(
% 0.18/0.38 ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[7])).
% 0.18/0.38 tff(9,plain,
% 0.18/0.38 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.38 tff(10,plain,
% 0.18/0.38 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(11,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.18/0.38 tff(12,plain,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(13,plain,
% 0.18/0.38 (^[B_2: $i] : refl((tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2))) <=> (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(14,plain,
% 0.18/0.38 (![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2))) <=> ![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[13])).
% 0.18/0.38 tff(15,plain,
% 0.18/0.38 (![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2))) <=> ![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(16,plain,
% 0.18/0.38 (^[B_2: $i] : rewrite((((~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2))) | tptp_fun__LE_(f(B_2), s(|'0'|))) <=> (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(17,plain,
% 0.18/0.38 (![B_2: $i] : (((~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2))) | tptp_fun__LE_(f(B_2), s(|'0'|))) <=> ![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.18/0.38 tff(18,axiom,(![B_2: $i] : (((~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2))) | tptp_fun__LE_(f(B_2), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_9')).
% 0.18/0.38 tff(19,plain,
% 0.18/0.38 (![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.18/0.38 tff(20,plain,
% 0.18/0.38 (![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.38 tff(21,plain,(
% 0.18/0.38 ![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))),
% 0.18/0.38 inference(skolemize,[status(sab)],[20])).
% 0.18/0.38 tff(22,plain,
% 0.18/0.38 (![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.18/0.38 tff(23,plain,
% 0.18/0.38 (((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | (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_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | 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'|)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(24,plain,
% 0.18/0.38 ((tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))) <=> (tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(25,plain,
% 0.18/0.38 (((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | (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'|))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[24])).
% 0.18/0.38 tff(26,plain,
% 0.18/0.38 (((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | 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'|)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[25, 23])).
% 0.18/0.38 tff(27,plain,
% 0.18/0.38 ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(28,plain,
% 0.18/0.38 ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | 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'|))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.38 tff(29,plain,
% 0.18/0.38 (tptp_fun__E_(s(|'0'|), f(suc(z))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[28, 22, 12])).
% 0.18/0.38 tff(30,plain,
% 0.18/0.38 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[29, 1])).
% 0.18/0.38 tff(31,assumption,(~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))), introduced(assumption)).
% 0.18/0.38 tff(32,plain,
% 0.18/0.38 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(33,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[32, 9, 31])).
% 0.18/0.38 tff(34,plain,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.38 tff(35,plain,
% 0.18/0.38 (^[B_2: $i] : refl((tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|))) <=> (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(36,plain,
% 0.18/0.38 (![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|))) <=> ![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[35])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 (![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|))) <=> ![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (^[B_2: $i] : rewrite((((~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_2))))) | tptp_fun__LE_(f(B_2), s(|'0'|))) <=> (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 (![B_2: $i] : (((~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_2))))) | tptp_fun__LE_(f(B_2), s(|'0'|))) <=> ![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[38])).
% 0.18/0.39 tff(40,axiom,(![B_2: $i] : (((~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_2))))) | tptp_fun__LE_(f(B_2), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_45')).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 (![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 (![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.18/0.39 tff(43,plain,(
% 0.18/0.39 ![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[42])).
% 0.18/0.39 tff(44,plain,
% 0.18/0.39 (![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 (((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))))) <=> ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(46,plain,
% 0.18/0.39 ((tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))) <=> (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(47,plain,
% 0.18/0.39 (((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))) <=> ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|))))))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[46])).
% 0.18/0.39 tff(48,plain,
% 0.18/0.39 (((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))) <=> ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))))),
% 0.18/0.39 inference(transitivity,[status(thm)],[47, 45])).
% 0.18/0.39 tff(49,plain,
% 0.18/0.39 ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(50,plain,
% 0.18/0.39 ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.18/0.39 tff(51,plain,
% 0.18/0.39 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[50, 44])).
% 0.18/0.39 tff(52,plain,
% 0.18/0.39 (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[51, 1, 34])).
% 0.18/0.39 tff(53,assumption,(~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 0.18/0.39 tff(54,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), introduced(assumption)).
% 0.18/0.39 tff(55,plain,
% 0.18/0.39 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(56,plain,
% 0.18/0.39 ($false),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[55, 9, 54])).
% 0.18/0.39 tff(57,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.39 tff(58,plain,
% 0.18/0.39 (^[B_2: $i] : refl((tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(59,plain,
% 0.18/0.39 (![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|))))) <=> ![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[58])).
% 0.18/0.39 tff(60,plain,
% 0.18/0.39 (![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|))))) <=> ![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(61,plain,
% 0.18/0.39 (^[B_2: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_2)))) | tptp_fun__LE_(f(B_2), s(|'0'|))) <=> (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(62,plain,
% 0.18/0.39 (![B_2: $i] : (((~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_2)))) | tptp_fun__LE_(f(B_2), s(|'0'|))) <=> ![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[61])).
% 0.18/0.39 tff(63,axiom,(![B_2: $i] : (((~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_2)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_32')).
% 0.18/0.39 tff(64,plain,
% 0.18/0.39 (![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.18/0.39 tff(65,plain,
% 0.18/0.39 (![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.18/0.39 tff(66,plain,(
% 0.18/0.39 ![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))))),
% 0.18/0.39 inference(skolemize,[status(sab)],[65])).
% 0.18/0.39 tff(67,plain,
% 0.18/0.39 (![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.18/0.39 tff(68,plain,
% 0.18/0.39 (((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), 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_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), 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'|)))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(69,plain,
% 0.18/0.39 ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), 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'|)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(70,plain,
% 0.18/0.39 ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), 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'|))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.18/0.39 tff(71,plain,
% 0.18/0.39 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[70, 67, 57])).
% 0.18/0.39 tff(72,plain,
% 0.18/0.39 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[71, 53])).
% 0.18/0.39 tff(73,plain,
% 0.18/0.39 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(74,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_24')).
% 0.18/0.39 tff(75,plain,
% 0.18/0.39 (~tptp_fun__LE_(f(z), |'0'|)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.18/0.39 tff(76,plain,
% 0.18/0.39 (^[B_5: $i] : refl((tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|)))) <=> (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(77,plain,
% 0.18/0.39 (![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|)))) <=> ![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.18/0.39 tff(78,plain,
% 0.18/0.39 (![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|)))) <=> ![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(79,plain,
% 0.18/0.39 (^[B_5: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_5)))) | tptp_fun__LE_(f(B_5), |'0'|)) <=> (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(80,plain,
% 0.18/0.39 (![B_5: $i] : (((~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_5)))) | tptp_fun__LE_(f(B_5), |'0'|)) <=> ![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[79])).
% 0.18/0.39 tff(81,axiom,(![B_5: $i] : (((~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_5)))) | tptp_fun__LE_(f(B_5), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_40')).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 (![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 (![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.18/0.40 tff(84,plain,(
% 0.18/0.40 ![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[83])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 (![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 (((~![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))) <=> ((~![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(87,plain,
% 0.18/0.40 ((~![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(88,plain,
% 0.18/0.40 ((~![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_5))) | (~tptp_fun__LE_(f(suc(B_5)), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[88, 85, 75])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[89, 72])).
% 0.18/0.40 tff(91,plain,
% 0.18/0.40 (((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))) <=> ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 ((tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) <=> (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 (((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[92])).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 (((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[93, 91])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[96, 22, 57])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[97, 53])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 (^[B_5: $i] : refl((tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|)))) <=> (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 (![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|)))) <=> ![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 (![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|)))) <=> ![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (^[B_5: $i] : rewrite((((~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_5))))) | tptp_fun__LE_(f(B_5), |'0'|)) <=> (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 (![B_5: $i] : (((~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_5))))) | tptp_fun__LE_(f(B_5), |'0'|)) <=> ![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[102])).
% 0.18/0.40 tff(104,axiom,(![B_5: $i] : (((~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_5))))) | tptp_fun__LE_(f(B_5), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_51')).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.18/0.40 tff(106,plain,
% 0.18/0.40 (![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.18/0.40 tff(107,plain,(
% 0.18/0.40 ![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[106])).
% 0.18/0.40 tff(108,plain,
% 0.18/0.40 (![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[107, 100])).
% 0.18/0.40 tff(109,plain,
% 0.18/0.40 (((~![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))))) <=> ((~![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(110,plain,
% 0.18/0.40 ((~![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(111,plain,
% 0.18/0.40 ((~![B_5: $i] : (tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_5)))) | (~tptp_fun__LE_(f(suc(suc(B_5))), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.18/0.40 tff(112,plain,
% 0.18/0.40 (tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[111, 108, 75])).
% 0.18/0.40 tff(113,plain,
% 0.18/0.40 (tptp_fun__E_(|'0'|, f(suc(suc(z))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[112, 98])).
% 0.18/0.40 tff(114,assumption,(tptp_fun__E_(|'0'|, f(suc(z)))), introduced(assumption)).
% 0.18/0.40 tff(115,assumption,(tptp_fun__E_(|'0'|, f(suc(suc(z))))), introduced(assumption)).
% 0.18/0.40 tff(116,assumption,(~iLEQ(suc(z), suc(z))), introduced(assumption)).
% 0.18/0.40 tff(117,assumption,(~tptp_fun__LE_(f(z), s(|'0'|))), introduced(assumption)).
% 0.18/0.40 tff(118,plain,
% 0.18/0.40 (((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), 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_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), 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'|)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(119,plain,
% 0.18/0.40 ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), 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'|)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(120,plain,
% 0.18/0.40 ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), 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'|))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.18/0.40 tff(121,plain,
% 0.18/0.40 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[120, 67])).
% 0.18/0.40 tff(122,plain,
% 0.18/0.40 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[121, 117, 12])).
% 0.18/0.40 tff(123,plain,
% 0.18/0.40 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(124,plain,
% 0.18/0.40 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[123, 9])).
% 0.18/0.40 tff(125,plain,
% 0.18/0.40 (((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))) <=> ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(126,plain,
% 0.18/0.40 ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(127,plain,
% 0.18/0.40 ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | (~tptp_fun__LE_(f(B_2), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_2)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.18/0.40 tff(128,plain,
% 0.18/0.40 (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[127, 22])).
% 0.18/0.40 tff(129,plain,
% 0.18/0.40 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[128, 124])).
% 0.18/0.40 tff(130,plain,
% 0.18/0.40 (tptp_fun__E_(s(|'0'|), f(z))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[129, 117])).
% 0.18/0.40 tff(131,plain,
% 0.18/0.40 (((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))) <=> ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(132,plain,
% 0.18/0.40 ((tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(z), s(|'0'|))) <=> (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(133,plain,
% 0.18/0.40 (((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(z), s(|'0'|)))) <=> ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[132])).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 (((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(z), s(|'0'|)))) <=> ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[133, 131])).
% 0.18/0.41 tff(135,plain,
% 0.18/0.41 ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(z), s(|'0'|)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(136,plain,
% 0.18/0.41 ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.18/0.41 tff(137,plain,
% 0.18/0.41 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[136, 44])).
% 0.18/0.41 tff(138,plain,
% 0.18/0.41 (tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[137, 117, 57])).
% 0.18/0.41 tff(139,assumption,(tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 0.18/0.41 tff(140,assumption,(tptp_fun__E_(s(|'0'|), f(z))), introduced(assumption)).
% 0.18/0.41 tff(141,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 0.18/0.41 tff(142,plain,
% 0.18/0.41 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(143,plain,
% 0.18/0.41 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[142])).
% 0.18/0.41 tff(144,plain,
% 0.18/0.41 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(145,plain,
% 0.18/0.41 (^[A_1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | iLEQ(suc(A_1), suc(A_1))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(146,plain,
% 0.18/0.41 (![A_1: $i] : (((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[145])).
% 0.18/0.41 tff(147,axiom,(![A_1: $i] : (((((~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_5')).
% 0.18/0.41 tff(148,plain,
% 0.18/0.41 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.18/0.41 tff(149,plain,
% 0.18/0.41 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.18/0.41 tff(150,plain,(
% 0.18/0.41 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[149])).
% 0.18/0.41 tff(151,plain,
% 0.18/0.41 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.18/0.41 tff(152,plain,
% 0.18/0.41 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z)))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(153,plain,
% 0.18/0.41 ((iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(f(z), 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_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(154,plain,
% 0.18/0.41 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[153])).
% 0.18/0.41 tff(155,plain,
% 0.18/0.41 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[154, 152])).
% 0.18/0.41 tff(156,plain,
% 0.18/0.41 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(157,plain,
% 0.18/0.41 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.18/0.41 tff(158,plain,
% 0.18/0.41 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[157, 151])).
% 0.18/0.41 tff(159,plain,
% 0.18/0.41 (~tptp_fun__E_(f(z), f(suc(z)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[158, 116, 141, 140, 139])).
% 0.18/0.41 tff(160,plain,
% 0.18/0.41 (^[A_1: $i] : refl((tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(161,plain,
% 0.18/0.41 (![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[160])).
% 0.18/0.41 tff(162,plain,
% 0.18/0.41 (![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(163,plain,
% 0.18/0.41 (^[A_1: $i] : trans(monotonicity(rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))), (((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> ((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1))))), rewrite(((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))), (((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(164,plain,
% 0.18/0.42 (![A_1: $i] : ((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> ![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[163])).
% 0.18/0.42 tff(165,axiom,(![A_1: $i] : ((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_23')).
% 0.18/0.42 tff(166,plain,
% 0.18/0.42 (![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.18/0.42 tff(167,plain,
% 0.18/0.42 (![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.18/0.42 tff(168,plain,(
% 0.18/0.42 ![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[167])).
% 0.18/0.42 tff(169,plain,
% 0.18/0.42 (![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[168, 161])).
% 0.18/0.42 tff(170,plain,
% 0.18/0.42 (((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z)))) <=> ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(171,plain,
% 0.18/0.42 ((tptp_fun__E_(f(z), f(suc(z))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(172,plain,
% 0.18/0.42 (((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (tptp_fun__E_(f(z), f(suc(z))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[171])).
% 0.18/0.42 tff(173,plain,
% 0.18/0.42 (((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (tptp_fun__E_(f(z), f(suc(z))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.42 inference(transitivity,[status(thm)],[172, 170])).
% 0.18/0.42 tff(174,plain,
% 0.18/0.42 ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (tptp_fun__E_(f(z), f(suc(z))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(175,plain,
% 0.18/0.42 ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.18/0.42 tff(176,plain,
% 0.18/0.42 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | iLEQ(suc(z), suc(z))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[175, 169])).
% 0.18/0.42 tff(177,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[176, 159, 116, 140, 139])).
% 0.18/0.42 tff(178,plain,(iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.42 tff(179,plain,
% 0.18/0.42 (iLEQ(suc(z), suc(z))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[178, 130, 122, 138])).
% 0.18/0.42 tff(180,plain,
% 0.18/0.42 (^[A_1: $i, B_3: $i] : refl(((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(181,plain,
% 0.18/0.42 (![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) <=> ![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[180])).
% 0.18/0.42 tff(182,plain,
% 0.18/0.42 (![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) <=> ![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(183,plain,
% 0.18/0.42 (^[A_1: $i, B_3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))))), (((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) <=> (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))), (((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))))), ((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))), ((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))))), (((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))), (((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))))), ((((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))), ((((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))))), (((((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) | (~tptp_fun__E_(f(B_3), f(suc(B_3))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(f(B_3), f(suc(B_3))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(f(B_3), f(suc(B_3))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))), (((((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) | (~tptp_fun__E_(f(B_3), f(suc(B_3))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))))), ((((((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) | (~tptp_fun__E_(f(B_3), f(suc(B_3))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))), ((((((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) | (~tptp_fun__E_(f(B_3), f(suc(B_3))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(184,plain,
% 0.18/0.43 (![A_1: $i, B_3: $i] : (((((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) | (~tptp_fun__E_(f(B_3), f(suc(B_3))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[183])).
% 0.18/0.43 tff(185,axiom,(![A_1: $i, B_3: $i] : (((((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) | (~tptp_fun__E_(f(B_3), f(suc(B_3))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_33')).
% 0.18/0.43 tff(186,plain,
% 0.18/0.43 (![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.18/0.43 tff(187,plain,
% 0.18/0.43 (![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.18/0.43 tff(188,plain,(
% 0.18/0.43 ![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))),
% 0.18/0.43 inference(skolemize,[status(sab)],[187])).
% 0.18/0.43 tff(189,plain,
% 0.18/0.43 (![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.18/0.43 tff(190,plain,
% 0.18/0.43 (((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(191,plain,
% 0.18/0.43 (((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(z), 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_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(192,plain,
% 0.18/0.43 (((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[191])).
% 0.18/0.43 tff(193,plain,
% 0.18/0.43 (((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[192, 190])).
% 0.18/0.43 tff(194,plain,
% 0.18/0.43 ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(195,plain,
% 0.18/0.43 ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.18/0.43 tff(196,plain,
% 0.18/0.43 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[195, 189])).
% 0.18/0.43 tff(197,plain,
% 0.18/0.43 (~tptp_fun__E_(f(z), f(suc(z)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[196, 179, 138, 130, 122])).
% 0.18/0.43 tff(198,plain,
% 0.18/0.43 (^[A_1: $i, B_3: $i] : refl((tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(199,plain,
% 0.18/0.43 (![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) <=> ![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[198])).
% 0.18/0.43 tff(200,plain,
% 0.18/0.43 (![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) <=> ![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(201,plain,
% 0.18/0.43 (^[A_1: $i, B_3: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))), ((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))), ((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))))), (((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))), (((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))))), ((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))), ((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))))), (((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))), (((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))))), ((((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_3), f(suc(B_3)))) <=> ((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) | tptp_fun__E_(f(B_3), f(suc(B_3)))))), rewrite(((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3)))) | tptp_fun__E_(f(B_3), f(suc(B_3)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))), ((((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_3), f(suc(B_3)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(202,plain,
% 0.18/0.44 (![A_1: $i, B_3: $i] : (((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_3), f(suc(B_3)))) <=> ![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[201])).
% 0.18/0.44 tff(203,axiom,(![A_1: $i, B_3: $i] : (((((((~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(B_3)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_3), f(suc(B_3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_52')).
% 0.18/0.44 tff(204,plain,
% 0.18/0.44 (![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.18/0.44 tff(205,plain,
% 0.18/0.44 (![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.18/0.44 tff(206,plain,(
% 0.18/0.44 ![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))),
% 0.18/0.44 inference(skolemize,[status(sab)],[205])).
% 0.18/0.44 tff(207,plain,
% 0.18/0.44 (![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[206, 199])).
% 0.18/0.44 tff(208,plain,
% 0.18/0.44 (((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(209,plain,
% 0.18/0.44 ((tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(210,plain,
% 0.18/0.44 (((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[209])).
% 0.18/0.44 tff(211,plain,
% 0.18/0.44 (((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.44 inference(transitivity,[status(thm)],[210, 208])).
% 0.18/0.44 tff(212,plain,
% 0.18/0.44 ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(213,plain,
% 0.18/0.44 ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.18/0.44 tff(214,plain,
% 0.18/0.44 ((~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[213, 207])).
% 0.18/0.44 tff(215,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[214, 197, 179, 130, 122])).
% 0.18/0.44 tff(216,plain,(tptp_fun__LE_(f(z), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.44 tff(217,plain,
% 0.18/0.44 (^[B_5: $i] : refl(((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5))) <=> ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(218,plain,
% 0.18/0.44 (![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5))) <=> ![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[217])).
% 0.18/0.44 tff(219,plain,
% 0.18/0.44 (![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5))) <=> ![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(220,plain,
% 0.18/0.44 (^[B_5: $i] : rewrite((((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_5))) | tptp_fun__LE_(f(B_5), |'0'|)) <=> ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(221,plain,
% 0.18/0.44 (![B_5: $i] : (((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_5))) | tptp_fun__LE_(f(B_5), |'0'|)) <=> ![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[220])).
% 0.18/0.44 tff(222,axiom,(![B_5: $i] : (((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_5))) | tptp_fun__LE_(f(B_5), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_34')).
% 0.18/0.44 tff(223,plain,
% 0.18/0.44 (![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.18/0.44 tff(224,plain,
% 0.18/0.44 (![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[223, 219])).
% 0.18/0.45 tff(225,plain,(
% 0.18/0.45 ![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))),
% 0.18/0.45 inference(skolemize,[status(sab)],[224])).
% 0.18/0.45 tff(226,plain,
% 0.18/0.45 (![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[225, 218])).
% 0.18/0.45 tff(227,plain,
% 0.18/0.45 (((~![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(228,plain,
% 0.18/0.45 (((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z))) <=> (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(229,plain,
% 0.18/0.45 (((~![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[228])).
% 0.18/0.45 tff(230,plain,
% 0.18/0.45 (((~![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[229, 227])).
% 0.18/0.45 tff(231,plain,
% 0.18/0.45 ((~![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(232,plain,
% 0.18/0.45 ((~![B_5: $i] : ((~tptp_fun__LE_(f(B_5), s(|'0'|))) | tptp_fun__LE_(f(B_5), |'0'|) | tptp_fun__E_(|'0'|, f(B_5)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.18/0.45 tff(233,plain,
% 0.18/0.45 ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[232, 226, 75])).
% 0.18/0.45 tff(234,plain,
% 0.18/0.45 (tptp_fun__E_(|'0'|, f(z))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[233, 216])).
% 0.18/0.45 tff(235,plain,
% 0.18/0.45 (^[A_2: $i] : refl((tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(236,plain,
% 0.18/0.45 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> ![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[235])).
% 0.18/0.45 tff(237,plain,
% 0.18/0.45 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> ![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(238,plain,
% 0.18/0.45 (^[A_2: $i] : trans(monotonicity(rewrite((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) <=> (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> ((tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))))), rewrite(((tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | iLEQ(suc(A_2), suc(A_2))) <=> (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))), (((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(239,plain,
% 0.18/0.45 (![A_2: $i] : ((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> ![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[238])).
% 0.18/0.45 tff(240,axiom,(![A_2: $i] : ((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_26')).
% 0.18/0.45 tff(241,plain,
% 0.18/0.45 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.18/0.45 tff(242,plain,
% 0.18/0.45 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[241, 237])).
% 0.18/0.45 tff(243,plain,(
% 0.18/0.45 ![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))),
% 0.18/0.45 inference(skolemize,[status(sab)],[242])).
% 0.18/0.45 tff(244,plain,
% 0.18/0.45 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[243, 236])).
% 0.18/0.45 tff(245,plain,
% 0.18/0.45 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))) | (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z)))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(246,plain,
% 0.18/0.45 ((tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z))) <=> (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(247,plain,
% 0.18/0.45 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))) | (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))) | (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[246])).
% 0.18/0.45 tff(248,plain,
% 0.18/0.45 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))) | (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[247, 245])).
% 0.18/0.45 tff(249,plain,
% 0.18/0.45 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))) | (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(250,plain,
% 0.18/0.45 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.18/0.45 tff(251,plain,
% 0.18/0.45 (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[250, 244])).
% 0.18/0.45 tff(252,plain,
% 0.18/0.45 (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[251, 234])).
% 0.18/0.45 tff(253,plain,
% 0.18/0.45 (tptp_fun__E_(f(z), f(suc(z)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[252, 116, 114])).
% 0.18/0.45 tff(254,plain,
% 0.18/0.45 (^[A_2: $i] : refl(((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(255,plain,
% 0.18/0.45 (![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) <=> ![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[254])).
% 0.18/0.45 tff(256,plain,
% 0.18/0.45 (![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) <=> ![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(257,plain,
% 0.18/0.45 (^[A_2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))), ((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))), ((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))))), (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))), (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> (((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | iLEQ(suc(A_2), suc(A_2))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | iLEQ(suc(A_2), suc(A_2))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(258,plain,
% 0.18/0.45 (![A_2: $i] : (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | iLEQ(suc(A_2), suc(A_2))) <=> ![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[257])).
% 0.18/0.45 tff(259,axiom,(![A_2: $i] : (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | iLEQ(suc(A_2), suc(A_2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_41')).
% 0.18/0.45 tff(260,plain,
% 0.18/0.45 (![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.18/0.45 tff(261,plain,
% 0.18/0.45 (![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.18/0.45 tff(262,plain,(
% 0.18/0.45 ![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))),
% 0.18/0.45 inference(skolemize,[status(sab)],[261])).
% 0.18/0.45 tff(263,plain,
% 0.18/0.45 (![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[262, 255])).
% 0.18/0.45 tff(264,plain,
% 0.18/0.45 (((~![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))) | ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z)))) <=> ((~![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(265,plain,
% 0.18/0.45 (((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z)))))) <=> ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(266,plain,
% 0.18/0.45 (((~![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))) <=> ((~![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))) | ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[265])).
% 0.18/0.45 tff(267,plain,
% 0.18/0.45 (((~![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))) <=> ((~![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[266, 264])).
% 0.18/0.45 tff(268,plain,
% 0.18/0.45 ((~![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))) | ((~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(269,plain,
% 0.18/0.45 ((~![A_2: $i] : ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.18/0.45 tff(270,plain,
% 0.18/0.45 ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[269, 263])).
% 0.18/0.45 tff(271,plain,
% 0.18/0.45 ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[270, 234])).
% 0.18/0.46 tff(272,plain,
% 0.18/0.46 ($false),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[271, 253, 116, 115, 114])).
% 0.18/0.46 tff(273,plain,(iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.46 tff(274,plain,
% 0.18/0.46 (iLEQ(suc(z), suc(z))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[273, 113, 90])).
% 0.18/0.46 tff(275,plain,
% 0.18/0.46 (^[B_6: $i, A_2: $i] : refl(((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(276,plain,
% 0.18/0.46 (![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) <=> ![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[275])).
% 0.18/0.46 tff(277,plain,
% 0.18/0.46 (![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) <=> ![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(278,plain,
% 0.18/0.46 (^[B_6: $i, A_2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))), (((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))), (((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) <=> (((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~iLEQ(suc(A_2), suc(B_6)))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~iLEQ(suc(A_2), suc(B_6)))) <=> ((~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) <=> ((~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) <=> (((~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(B_6)))))), rewrite((((~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(B_6)))) <=> ((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) <=> ((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> (((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> ((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> ((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6))))) <=> (((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6))))) <=> ((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6))))) <=> ((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6))))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) <=> (((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6))))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(279,plain,
% 0.18/0.46 (![B_6: $i, A_2: $i] : (((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6))))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) <=> ![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[278])).
% 0.18/0.46 tff(280,axiom,(![B_6: $i, A_2: $i] : (((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6))))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_43')).
% 0.18/0.46 tff(281,plain,
% 0.18/0.46 (![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.18/0.46 tff(282,plain,
% 0.18/0.46 (![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[281, 277])).
% 0.18/0.46 tff(283,plain,(
% 0.18/0.46 ![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))),
% 0.18/0.46 inference(skolemize,[status(sab)],[282])).
% 0.18/0.46 tff(284,plain,
% 0.18/0.46 (![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[283, 276])).
% 0.18/0.46 tff(285,plain,
% 0.18/0.46 (((~![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))) | ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(286,plain,
% 0.18/0.46 (((~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(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z)))))) <=> ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(287,plain,
% 0.18/0.46 (((~![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))) | ((~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(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))) <=> ((~![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))) | ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.18/0.46 inference(monotonicity,[status(thm)],[286])).
% 0.18/0.46 tff(288,plain,
% 0.18/0.46 (((~![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))) | ((~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(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))) <=> ((~![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.46 inference(transitivity,[status(thm)],[287, 285])).
% 0.18/0.46 tff(289,plain,
% 0.18/0.46 ((~![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))) | ((~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(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))),
% 0.18/0.46 inference(quant_inst,[status(thm)],[])).
% 0.18/0.46 tff(290,plain,
% 0.18/0.46 ((~![B_6: $i, A_2: $i] : ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(f(B_6), f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_6))))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.18/0.46 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.18/0.46 tff(291,plain,
% 0.18/0.46 ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[290, 284])).
% 0.18/0.46 tff(292,plain,
% 0.18/0.46 ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[291, 234])).
% 0.18/0.46 tff(293,plain,
% 0.18/0.46 (~tptp_fun__E_(f(z), f(suc(z)))),
% 0.18/0.46 inference(unit_resolution,[status(thm)],[292, 274, 90, 113])).
% 0.18/0.46 tff(294,plain,
% 0.18/0.46 (^[B_6: $i, A_2: $i] : refl((tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))),
% 0.18/0.46 inference(bind,[status(th)],[])).
% 0.18/0.46 tff(295,plain,
% 0.18/0.46 (![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.18/0.46 inference(quant_intro,[status(thm)],[294])).
% 0.18/0.46 tff(296,plain,
% 0.18/0.46 (![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.18/0.46 inference(rewrite,[status(thm)],[])).
% 0.18/0.46 tff(297,plain,
% 0.18/0.46 (^[B_6: $i, A_2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) <=> (((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_6)))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_6)))) <=> ((~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) <=> ((~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), (((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) <=> (((~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(B_6)))))), rewrite((((~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(B_6)))) <=> ((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) <=> ((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) <=> (((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) <=> (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) <=> (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_6), f(suc(B_6)))) <=> ((tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(B_6), f(suc(B_6)))))), rewrite(((tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(B_6), f(suc(B_6)))) <=> (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_6), f(suc(B_6)))) <=> (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))))),
% 0.18/0.47 inference(bind,[status(th)],[])).
% 0.18/0.47 tff(298,plain,
% 0.18/0.47 (![B_6: $i, A_2: $i] : (((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_6), f(suc(B_6)))) <=> ![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.18/0.47 inference(quant_intro,[status(thm)],[297])).
% 0.18/0.47 tff(299,axiom,(![B_6: $i, A_2: $i] : (((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~iLEQ(suc(A_2), suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6)))) | (~tptp_fun__E_(|'0'|, f(suc(B_6))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_6), f(suc(B_6))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_10')).
% 0.18/0.47 tff(300,plain,
% 0.18/0.47 (![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.18/0.47 tff(301,plain,
% 0.18/0.47 (![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[300, 296])).
% 0.18/0.47 tff(302,plain,(
% 0.18/0.47 ![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.18/0.47 inference(skolemize,[status(sab)],[301])).
% 0.18/0.47 tff(303,plain,
% 0.18/0.47 (![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[302, 295])).
% 0.18/0.47 tff(304,plain,
% 0.18/0.47 (((~![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(305,plain,
% 0.18/0.47 ((tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~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(suc(z))))) <=> (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(306,plain,
% 0.18/0.47 (((~![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~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(suc(z)))))) <=> ((~![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[305])).
% 0.18/0.47 tff(307,plain,
% 0.18/0.47 (((~![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~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(suc(z)))))) <=> ((~![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[306, 304])).
% 0.18/0.47 tff(308,plain,
% 0.18/0.47 ((~![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~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(suc(z)))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(309,plain,
% 0.18/0.47 ((~![B_6: $i, A_2: $i] : (tptp_fun__E_(f(B_6), f(suc(B_6))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_6)))) | (~tptp_fun__E_(|'0'|, f(B_6))) | (~iLEQ(suc(A_2), suc(B_6))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.18/0.47 tff(310,plain,
% 0.18/0.47 (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[309, 303])).
% 0.18/0.47 tff(311,plain,
% 0.18/0.47 (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[310, 234])).
% 0.18/0.47 tff(312,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[311, 293, 274, 90])).
% 0.18/0.47 tff(313,plain,(tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(314,assumption,(~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))), introduced(assumption)).
% 0.18/0.47 tff(315,plain,
% 0.18/0.47 (((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(316,plain,
% 0.18/0.47 ((tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~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_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(317,plain,
% 0.18/0.47 (((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[316])).
% 0.18/0.47 tff(318,plain,
% 0.18/0.47 (((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[317, 315])).
% 0.18/0.47 tff(319,plain,
% 0.18/0.47 ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(320,plain,
% 0.18/0.47 ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.18/0.47 tff(321,plain,
% 0.18/0.47 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[320, 207])).
% 0.18/0.47 tff(322,plain,
% 0.18/0.47 (~iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[321, 314, 313, 139])).
% 0.18/0.47 tff(323,plain,
% 0.18/0.47 (((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))))) <=> ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(324,plain,
% 0.18/0.47 ((tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(325,plain,
% 0.18/0.47 (((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[324])).
% 0.18/0.47 tff(326,plain,
% 0.18/0.47 (((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.18/0.47 inference(transitivity,[status(thm)],[325, 323])).
% 0.18/0.47 tff(327,plain,
% 0.18/0.47 ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.18/0.47 inference(quant_inst,[status(thm)],[])).
% 0.18/0.47 tff(328,plain,
% 0.18/0.47 ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.18/0.47 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.18/0.47 tff(329,plain,
% 0.18/0.47 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[328, 169])).
% 0.18/0.47 tff(330,plain,
% 0.18/0.47 ($false),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[329, 322, 314, 313, 139])).
% 0.18/0.47 tff(331,plain,(tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.47 tff(332,plain,
% 0.18/0.47 (tptp_fun__E_(f(suc(z)), f(suc(suc(z))))),
% 0.18/0.47 inference(unit_resolution,[status(thm)],[331, 30])).
% 0.18/0.47 tff(333,plain,
% 0.18/0.47 (((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))) <=> ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(334,plain,
% 0.18/0.47 (((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(z)), 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(suc(z)))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.18/0.47 inference(rewrite,[status(thm)],[])).
% 0.18/0.47 tff(335,plain,
% 0.18/0.47 (((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(z)), 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(suc(z)))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))) <=> ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))))),
% 0.18/0.47 inference(monotonicity,[status(thm)],[334])).
% 0.18/0.47 tff(336,plain,
% 0.18/0.47 (((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(z)), 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(suc(z)))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))) <=> ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[335, 333])).
% 0.18/0.48 tff(337,plain,
% 0.18/0.48 ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(z)), 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(suc(z)))))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(338,plain,
% 0.18/0.48 ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[337, 336])).
% 0.18/0.48 tff(339,plain,
% 0.18/0.48 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[338, 189])).
% 0.18/0.48 tff(340,plain,
% 0.18/0.48 (~iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[339, 332, 313, 52, 30])).
% 0.18/0.48 tff(341,plain,
% 0.18/0.48 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(z)), suc(suc(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(342,plain,
% 0.18/0.48 ((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_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(343,plain,
% 0.18/0.48 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[342])).
% 0.18/0.48 tff(344,plain,
% 0.18/0.48 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[343, 341])).
% 0.18/0.48 tff(345,plain,
% 0.18/0.48 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(346,plain,
% 0.18/0.48 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.18/0.48 tff(347,plain,
% 0.18/0.48 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[346, 151])).
% 0.18/0.48 tff(348,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[347, 340, 332, 313, 52, 30])).
% 0.18/0.48 tff(349,plain,(tptp_fun__LE_(f(suc(z)), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(350,plain,
% 0.18/0.48 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[89, 349])).
% 0.18/0.48 tff(351,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))), introduced(assumption)).
% 0.18/0.48 tff(352,plain,
% 0.18/0.48 (((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))))) <=> ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(353,plain,
% 0.18/0.48 ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(354,plain,
% 0.18/0.48 ((~![B_2: $i] : (tptp_fun__LE_(f(B_2), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(B_2))) | (~tptp_fun__LE_(f(suc(B_2)), s(s(|'0'|)))))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.18/0.48 tff(355,plain,
% 0.18/0.48 (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[354, 67])).
% 0.18/0.48 tff(356,plain,
% 0.18/0.48 (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[355, 351, 34])).
% 0.18/0.48 tff(357,assumption,(~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))), introduced(assumption)).
% 0.18/0.48 tff(358,plain,
% 0.18/0.48 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(359,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[358, 9, 357])).
% 0.18/0.48 tff(360,plain,(tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(361,plain,
% 0.18/0.48 (((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))))) <=> ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(362,plain,
% 0.18/0.48 ((tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))) <=> (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(363,plain,
% 0.18/0.48 (((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))) <=> ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[362])).
% 0.18/0.48 tff(364,plain,
% 0.18/0.48 (((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))) <=> ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[363, 361])).
% 0.18/0.48 tff(365,plain,
% 0.18/0.48 ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(366,plain,
% 0.18/0.48 ((~![B_2: $i] : (tptp_fun__E_(s(|'0'|), f(suc(suc(B_2)))) | (~tptp_fun__LE_(f(suc(suc(B_2))), s(s(|'0'|)))) | tptp_fun__LE_(f(B_2), s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.18/0.48 tff(367,plain,
% 0.18/0.48 (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))) | (~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[366, 44])).
% 0.18/0.48 tff(368,plain,
% 0.18/0.48 (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[367, 351, 360])).
% 0.18/0.48 tff(369,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))), introduced(assumption)).
% 0.18/0.48 tff(370,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))), introduced(assumption)).
% 0.18/0.48 tff(371,assumption,(~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))), introduced(assumption)).
% 0.18/0.48 tff(372,plain,
% 0.18/0.48 (((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))) <=> ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(373,plain,
% 0.18/0.48 ((tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(374,plain,
% 0.18/0.48 (((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[373])).
% 0.18/0.48 tff(375,plain,
% 0.18/0.48 (((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[374, 372])).
% 0.18/0.48 tff(376,plain,
% 0.18/0.48 ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(377,plain,
% 0.18/0.48 ((~![A_1: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.18/0.48 tff(378,plain,
% 0.18/0.48 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[377, 169])).
% 0.18/0.48 tff(379,plain,
% 0.18/0.48 (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[378, 371, 141, 370])).
% 0.18/0.48 tff(380,plain,
% 0.18/0.48 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(381,plain,
% 0.18/0.48 ((iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(382,plain,
% 0.18/0.48 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.18/0.48 inference(monotonicity,[status(thm)],[381])).
% 0.18/0.48 tff(383,plain,
% 0.18/0.48 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.18/0.48 inference(transitivity,[status(thm)],[382, 380])).
% 0.18/0.48 tff(384,plain,
% 0.18/0.48 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))))),
% 0.18/0.48 inference(quant_inst,[status(thm)],[])).
% 0.18/0.48 tff(385,plain,
% 0.18/0.48 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.18/0.48 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.18/0.48 tff(386,plain,
% 0.18/0.48 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[385, 151])).
% 0.18/0.48 tff(387,plain,
% 0.18/0.48 ($false),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[386, 379, 371, 141, 370, 369])).
% 0.18/0.48 tff(388,plain,(iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.48 tff(389,plain,
% 0.18/0.48 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.18/0.48 inference(unit_resolution,[status(thm)],[388, 369, 370, 141])).
% 0.18/0.48 tff(390,plain,
% 0.18/0.48 (((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.48 tff(391,plain,
% 0.18/0.48 ((tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.18/0.48 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(392,plain,
% 0.18/0.49 (((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[391])).
% 0.18/0.49 tff(393,plain,
% 0.18/0.49 (((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[392, 390])).
% 0.18/0.49 tff(394,plain,
% 0.18/0.49 ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(395,plain,
% 0.18/0.49 ((~![A_1: $i, B_3: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | tptp_fun__E_(f(B_3), f(suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~iLEQ(suc(A_1), suc(B_3))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.18/0.49 tff(396,plain,
% 0.18/0.49 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[395, 207])).
% 0.18/0.49 tff(397,plain,
% 0.18/0.49 (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[396, 389, 141, 370])).
% 0.18/0.49 tff(398,plain,
% 0.18/0.49 (((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))) <=> ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(399,plain,
% 0.18/0.49 (((~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z)))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(400,plain,
% 0.18/0.49 (((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))))) <=> ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))))),
% 0.18/0.49 inference(monotonicity,[status(thm)],[399])).
% 0.18/0.49 tff(401,plain,
% 0.18/0.49 (((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))))) <=> ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[400, 398])).
% 0.18/0.49 tff(402,plain,
% 0.18/0.49 ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))))),
% 0.18/0.49 inference(quant_inst,[status(thm)],[])).
% 0.18/0.49 tff(403,plain,
% 0.18/0.49 ((~![A_1: $i, B_3: $i] : ((~tptp_fun__E_(s(|'0'|), f(suc(B_3)))) | (~tptp_fun__E_(s(|'0'|), f(B_3))) | (~tptp_fun__E_(f(B_3), f(suc(B_3)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~iLEQ(suc(A_1), suc(B_3))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_3))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.18/0.49 inference(modus_ponens,[status(thm)],[402, 401])).
% 0.18/0.49 tff(404,plain,
% 0.18/0.49 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[403, 189])).
% 0.18/0.49 tff(405,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[404, 397, 389, 141, 370, 369])).
% 0.18/0.49 tff(406,plain,((~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(407,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[406, 368, 356, 313])).
% 0.18/0.49 tff(408,plain,(tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.49 tff(409,plain,
% 0.18/0.49 (tptp_fun__E_(|'0'|, f(suc(suc(z))))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[112, 408])).
% 0.18/0.49 tff(410,plain,
% 0.18/0.49 (iLEQ(suc(z), suc(z))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[273, 409, 350])).
% 0.18/0.49 tff(411,plain,
% 0.18/0.49 (~tptp_fun__E_(f(z), f(suc(z)))),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[292, 410, 350, 409])).
% 0.18/0.49 tff(412,plain,
% 0.18/0.49 ($false),
% 0.18/0.49 inference(unit_resolution,[status(thm)],[311, 411, 410, 350])).
% 0.18/0.49 % SZS output end Proof
% 0.18/0.49 % E exiting
%------------------------------------------------------------------------------