%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO661-1 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:42:03 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO661-1 : TPTP v9.0.0. Released v7.3.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 13:21:25 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(tptp_fun__E__type, type, (
% 0.19/0.40 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.19/0.40 tff(f_type, type, (
% 0.19/0.40 f: $i > $i)).
% 0.19/0.40 tff(suc_type, type, (
% 0.19/0.40 suc: $i > $i)).
% 0.19/0.40 tff(z_type, type, (
% 0.19/0.40 z: $i)).
% 0.19/0.40 tff(iLEQ_type, type, (
% 0.19/0.40 iLEQ: ( $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun__0__type, type, (
% 0.19/0.40 tptp_fun__0_: $i)).
% 0.19/0.40 tff(tptp_fun__LE__type, type, (
% 0.19/0.40 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.19/0.40 tff(s_type, type, (
% 0.19/0.40 s: $i > $i)).
% 0.19/0.40 tff(1,assumption,(~tptp_fun__LE_(f(z), s(|'0'|))), introduced(assumption)).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(s(|'0'|))) <=> tptp_fun__LE_(f(A), s(s(|'0'|))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|))) <=> ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(5,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_72')).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.19/0.40 tff(7,plain,(
% 0.19/0.40 ![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[6])).
% 0.19/0.40 tff(8,plain,
% 0.19/0.40 (![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (tptp_fun__LE_(f(z), s(s(|'0'|)))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (^[B_10: $i] : refl((tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))) <=> (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (^[B_10: $i] : rewrite((((~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))) | tptp_fun__LE_(f(B_10), s(|'0'|))) <=> (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (![B_10: $i] : (((~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))) | tptp_fun__LE_(f(B_10), s(|'0'|))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.40 tff(16,axiom,(![B_10: $i] : (((~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10))) | tptp_fun__LE_(f(B_10), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_118')).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.19/0.40 tff(18,plain,
% 0.19/0.40 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.19/0.40 tff(19,plain,(
% 0.19/0.40 ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[18])).
% 0.19/0.40 tff(20,plain,
% 0.19/0.40 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(22,plain,
% 0.19/0.41 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.41 tff(24,plain,
% 0.19/0.41 (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(z), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[23, 20])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(z))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[24, 10])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (tptp_fun__E_(s(|'0'|), f(z))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[25, 1])).
% 0.19/0.41 tff(27,assumption,(~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), introduced(assumption)).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[28, 8, 27])).
% 0.19/0.41 tff(30,plain,(tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (^[B_10: $i] : refl((tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))) <=> (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(34,plain,
% 0.19/0.41 (^[B_10: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))) | tptp_fun__LE_(f(B_10), s(|'0'|))) <=> (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![B_10: $i] : (((~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))) | tptp_fun__LE_(f(B_10), s(|'0'|))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.41 tff(36,axiom,(![B_10: $i] : (((~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10)))) | tptp_fun__LE_(f(B_10), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_119')).
% 0.19/0.41 tff(37,plain,
% 0.19/0.41 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.41 tff(39,plain,(
% 0.19/0.41 ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[38])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (tptp_fun__LE_(f(z), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[43, 40])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[44, 30])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[45, 1])).
% 0.19/0.41 tff(47,assumption,(~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 0.19/0.41 tff(48,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), introduced(assumption)).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[49, 8, 48])).
% 0.19/0.41 tff(51,plain,(tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (^[B_10: $i] : refl((tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|))))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|))))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (^[B_10: $i] : rewrite((((~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10))))) | tptp_fun__LE_(f(B_10), s(|'0'|))) <=> (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![B_10: $i] : (((~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10))))) | tptp_fun__LE_(f(B_10), s(|'0'|))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.41 tff(57,axiom,(![B_10: $i] : (((~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10))))) | tptp_fun__LE_(f(B_10), s(|'0'|)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_33')).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.19/0.41 tff(60,plain,(
% 0.19/0.41 ![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[59])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(s(|'0'|)))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(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_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(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'|)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(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'|)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(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'|))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 (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'|))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[64, 61])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (tptp_fun__LE_(f(z), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[65, 51])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[66, 47])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 (^[B_17: $i] : refl((tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|)))) <=> (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|)))) <=> ![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|)))) <=> ![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (^[B_17: $i] : rewrite((((~tptp_fun__LE_(f(B_17), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_17))) | tptp_fun__LE_(f(B_17), |'0'|)) <=> (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (![B_17: $i] : (((~tptp_fun__LE_(f(B_17), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_17))) | tptp_fun__LE_(f(B_17), |'0'|)) <=> ![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.19/0.41 tff(73,axiom,(![B_17: $i] : (((~tptp_fun__LE_(f(B_17), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_17))) | tptp_fun__LE_(f(B_17), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_0')).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.19/0.41 tff(76,plain,(
% 0.19/0.41 ![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[75])).
% 0.19/0.41 tff(77,plain,
% 0.19/0.41 (![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.19/0.41 tff(78,plain,
% 0.19/0.41 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(79,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_93')).
% 0.19/0.41 tff(80,plain,
% 0.19/0.41 (~tptp_fun__LE_(f(z), |'0'|)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.41 tff(81,plain,
% 0.19/0.41 (((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(82,plain,
% 0.19/0.41 ((tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|)))) <=> (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(83,plain,
% 0.19/0.41 (((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[82])).
% 0.19/0.41 tff(84,plain,
% 0.19/0.41 (((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))) <=> ((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[83, 81])).
% 0.19/0.41 tff(85,plain,
% 0.19/0.41 ((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(z)) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 ((~![B_17: $i] : (tptp_fun__E_(|'0'|, f(B_17)) | tptp_fun__LE_(f(B_17), |'0'|) | (~tptp_fun__LE_(f(B_17), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (tptp_fun__E_(|'0'|, f(z)) | (~tptp_fun__LE_(f(z), s(|'0'|)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[86, 80, 77])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (tptp_fun__E_(|'0'|, f(z))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[87, 67])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 ((tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) <=> (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[90])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[91, 89])).
% 0.19/0.42 tff(93,plain,
% 0.19/0.42 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(94,plain,
% 0.19/0.42 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.42 tff(95,plain,
% 0.19/0.42 (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[94, 40])).
% 0.19/0.42 tff(96,plain,
% 0.19/0.42 (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[95, 51])).
% 0.19/0.42 tff(97,plain,
% 0.19/0.42 (tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[96, 47])).
% 0.19/0.42 tff(98,plain,
% 0.19/0.42 (^[B_17: $i] : refl((tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|)))) <=> (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(99,plain,
% 0.19/0.42 (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|)))) <=> ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[98])).
% 0.19/0.42 tff(100,plain,
% 0.19/0.42 (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|)))) <=> ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(101,plain,
% 0.19/0.42 (^[B_17: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_17)))) | tptp_fun__LE_(f(B_17), |'0'|)) <=> (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(102,plain,
% 0.19/0.42 (![B_17: $i] : (((~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_17)))) | tptp_fun__LE_(f(B_17), |'0'|)) <=> ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[101])).
% 0.19/0.42 tff(103,axiom,(![B_17: $i] : (((~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_17)))) | tptp_fun__LE_(f(B_17), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_57')).
% 0.19/0.42 tff(104,plain,
% 0.19/0.42 (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.42 tff(105,plain,
% 0.19/0.42 (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.19/0.42 tff(106,plain,(
% 0.19/0.42 ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[105])).
% 0.19/0.42 tff(107,plain,
% 0.19/0.42 (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.19/0.42 tff(108,plain,
% 0.19/0.42 (((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))) <=> ((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(109,plain,
% 0.19/0.42 ((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))) | (tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(110,plain,
% 0.19/0.42 ((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(B_17))) | (~tptp_fun__LE_(f(suc(B_17)), s(|'0'|))))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.42 tff(111,plain,
% 0.19/0.42 (tptp_fun__E_(|'0'|, f(suc(z))) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[110, 80, 107])).
% 0.19/0.42 tff(112,plain,
% 0.19/0.42 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[111, 97])).
% 0.19/0.42 tff(113,assumption,(~iLEQ(suc(z), suc(z))), introduced(assumption)).
% 0.19/0.42 tff(114,assumption,(tptp_fun__E_(|'0'|, f(z))), introduced(assumption)).
% 0.19/0.42 tff(115,plain,
% 0.19/0.42 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(116,plain,
% 0.19/0.42 ((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__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(117,plain,
% 0.19/0.42 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (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_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[116])).
% 0.19/0.42 tff(118,plain,
% 0.19/0.42 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (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_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[117, 115])).
% 0.19/0.42 tff(119,plain,
% 0.19/0.42 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (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)))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(120,plain,
% 0.19/0.42 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.19/0.42 tff(121,plain,
% 0.19/0.42 (tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[120, 20, 51])).
% 0.19/0.42 tff(122,plain,
% 0.19/0.42 (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[121, 47])).
% 0.19/0.42 tff(123,plain,
% 0.19/0.42 (^[B_17: $i] : refl((tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|)))) <=> (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(124,plain,
% 0.19/0.42 (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|)))) <=> ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[123])).
% 0.19/0.42 tff(125,plain,
% 0.19/0.42 (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|)))) <=> ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(126,plain,
% 0.19/0.42 (^[B_17: $i] : rewrite((((~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_17))))) | tptp_fun__LE_(f(B_17), |'0'|)) <=> (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|)))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(127,plain,
% 0.19/0.43 (![B_17: $i] : (((~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_17))))) | tptp_fun__LE_(f(B_17), |'0'|)) <=> ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.43 tff(128,axiom,(![B_17: $i] : (((~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_17))))) | tptp_fun__LE_(f(B_17), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_51')).
% 0.19/0.43 tff(129,plain,
% 0.19/0.43 (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.19/0.43 tff(130,plain,
% 0.19/0.43 (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.19/0.43 tff(131,plain,(
% 0.19/0.43 ![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[130])).
% 0.19/0.43 tff(132,plain,
% 0.19/0.43 (![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), s(|'0'|))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.19/0.43 tff(133,plain,
% 0.19/0.43 (((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), 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_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), 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'|))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(134,plain,
% 0.19/0.43 ((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), 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'|))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(135,plain,
% 0.19/0.43 ((~![B_17: $i] : (tptp_fun__LE_(f(B_17), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_17)))) | (~tptp_fun__LE_(f(suc(suc(B_17))), 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'|)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.19/0.43 tff(136,plain,
% 0.19/0.43 (tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[135, 80, 132])).
% 0.19/0.43 tff(137,plain,
% 0.19/0.43 (tptp_fun__E_(|'0'|, f(suc(suc(z))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[136, 122])).
% 0.19/0.43 tff(138,plain,
% 0.19/0.43 (^[A_2: $i] : refl((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_(f(A_2), f(suc(A_2))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(139,plain,
% 0.19/0.43 (![A_2: $i] : (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))))) <=> ![A_2: $i] : (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)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[138])).
% 0.19/0.43 tff(140,plain,
% 0.19/0.43 (![A_2: $i] : (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))))) <=> ![A_2: $i] : (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)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(141,plain,
% 0.19/0.43 (^[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))) <=> (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)))))), (((((~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))) <=> (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)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(142,plain,
% 0.19/0.43 (![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] : (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)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[141])).
% 0.19/0.43 tff(143,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_109')).
% 0.19/0.43 tff(144,plain,
% 0.19/0.43 (![A_2: $i] : (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)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.19/0.43 tff(145,plain,
% 0.19/0.43 (![A_2: $i] : (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)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.19/0.43 tff(146,plain,(
% 0.19/0.43 ![A_2: $i] : (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)))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[145])).
% 0.19/0.43 tff(147,plain,
% 0.19/0.43 (![A_2: $i] : (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)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.19/0.43 tff(148,plain,
% 0.19/0.43 (((~![A_2: $i] : (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(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_2: $i] : (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(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(149,plain,
% 0.19/0.43 ((~![A_2: $i] : (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(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(150,plain,
% 0.19/0.43 ((~![A_2: $i] : (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(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.19/0.43 tff(151,plain,
% 0.19/0.43 (iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[150, 147])).
% 0.19/0.43 tff(152,plain,
% 0.19/0.43 (tptp_fun__E_(f(z), f(suc(z)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[151, 112, 114, 113])).
% 0.19/0.43 tff(153,plain,
% 0.19/0.43 (^[A_2: $i] : refl((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))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(154,plain,
% 0.19/0.43 (![A_2: $i] : (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))))) <=> ![A_2: $i] : (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)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[153])).
% 0.19/0.43 tff(155,plain,
% 0.19/0.43 (![A_2: $i] : (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))))) <=> ![A_2: $i] : (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)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(156,plain,
% 0.19/0.43 (^[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(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(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(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))))), rewrite((((~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_(f(A_2), f(suc(A_2)))) | (~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(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(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(A_2))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(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(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))))), rewrite((((~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(A_2))))) | (~tptp_fun__E_(|'0'|, f(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)))))), (((((~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_(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))))))), ((((((~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_(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))))), rewrite((((~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))) <=> (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)))))), ((((((~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))) <=> (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)))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(157,plain,
% 0.19/0.43 (![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] : (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)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[156])).
% 0.19/0.43 tff(158,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_148')).
% 0.19/0.43 tff(159,plain,
% 0.19/0.43 (![A_2: $i] : (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)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.43 tff(160,plain,
% 0.19/0.43 (![A_2: $i] : (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)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.19/0.43 tff(161,plain,(
% 0.19/0.43 ![A_2: $i] : (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)))))),
% 0.19/0.43 inference(skolemize,[status(sab)],[160])).
% 0.19/0.43 tff(162,plain,
% 0.19/0.43 (![A_2: $i] : (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)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.19/0.43 tff(163,plain,
% 0.19/0.43 (((~![A_2: $i] : (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(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_2: $i] : (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(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(164,plain,
% 0.19/0.43 ((~![A_2: $i] : (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(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(165,plain,
% 0.19/0.43 ((~![A_2: $i] : (iLEQ(suc(A_2), suc(A_2)) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.19/0.44 tff(166,plain,
% 0.19/0.44 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[165, 162])).
% 0.19/0.44 tff(167,plain,
% 0.19/0.44 ($false),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[166, 152, 137, 114, 113, 112])).
% 0.19/0.44 tff(168,plain,(tptp_fun__E_(s(|'0'|), f(suc(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.44 tff(169,plain,
% 0.19/0.44 (iLEQ(suc(z), suc(z))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[168, 88, 47])).
% 0.19/0.44 tff(170,plain,
% 0.19/0.44 (^[B_18: $i, A_2: $i, B_19: $i] : refl((tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(171,plain,
% 0.19/0.44 (![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[170])).
% 0.19/0.44 tff(172,plain,
% 0.19/0.44 (![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(173,plain,
% 0.19/0.44 (^[B_18: $i, A_2: $i, B_19: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(B_18), suc(B_19)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(B_18), suc(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), (((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(B_19)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(B_18)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_18)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~iLEQ(suc(A_2), suc(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(A_2), f(suc(A_2)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~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))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) <=> (tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) <=> ((tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(B_18), f(suc(B_18)))))), rewrite(((tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) <=> (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) <=> (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) | tptp_fun__E_(f(B_19), f(suc(B_19)))) <=> ((tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(B_19), f(suc(B_19)))))), rewrite(((tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | tptp_fun__E_(f(B_19), f(suc(B_19)))) <=> (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) | tptp_fun__E_(f(B_19), f(suc(B_19)))) <=> (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(174,plain,
% 0.19/0.45 (![B_18: $i, A_2: $i, B_19: $i] : (((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) | tptp_fun__E_(f(B_19), f(suc(B_19)))) <=> ![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[173])).
% 0.19/0.45 tff(175,axiom,(![B_18: $i, A_2: $i, B_19: $i] : (((((((((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~iLEQ(suc(A_2), suc(B_18)))) | tptp_fun__E_(f(A_2), f(suc(A_2)))) | tptp_fun__E_(f(B_18), f(suc(B_18)))) | tptp_fun__E_(f(B_19), f(suc(B_19))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_20')).
% 0.19/0.45 tff(176,plain,
% 0.19/0.45 (![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.19/0.45 tff(177,plain,
% 0.19/0.45 (![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.19/0.45 tff(178,plain,(
% 0.19/0.45 ![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.19/0.45 inference(skolemize,[status(sab)],[177])).
% 0.19/0.45 tff(179,plain,
% 0.19/0.45 (![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.19/0.45 tff(180,plain,
% 0.19/0.45 (((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(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))))) <=> ((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(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))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(181,plain,
% 0.19/0.45 ((tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), 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))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z))))) <=> (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(182,plain,
% 0.19/0.45 (((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), 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))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(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)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[181])).
% 0.19/0.45 tff(183,plain,
% 0.19/0.45 (((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), 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))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(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))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[182, 180])).
% 0.19/0.45 tff(184,plain,
% 0.19/0.45 ((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), 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))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(185,plain,
% 0.19/0.45 ((~![B_18: $i, A_2: $i, B_19: $i] : (tptp_fun__E_(f(B_18), f(suc(B_18))) | tptp_fun__E_(f(A_2), f(suc(A_2))) | (~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | tptp_fun__E_(f(B_19), f(suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(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)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.19/0.45 tff(186,plain,
% 0.19/0.45 (tptp_fun__E_(f(z), f(suc(z)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[185, 179, 88, 112, 169])).
% 0.19/0.45 tff(187,plain,
% 0.19/0.45 (^[B_18: $i, A_2: $i, B_19: $i] : refl(((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(188,plain,
% 0.19/0.45 (![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) <=> ![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[187])).
% 0.19/0.45 tff(189,plain,
% 0.19/0.45 (![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) <=> ![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(190,plain,
% 0.19/0.45 (^[B_18: $i, A_2: $i, B_19: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~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_(|'0'|, f(suc(suc(B_18))))))), ((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~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_(|'0'|, f(suc(suc(B_18)))))))), (((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), (((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~iLEQ(suc(B_18), suc(B_19)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~iLEQ(suc(B_18), suc(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(B_19)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(B_18)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) | (~iLEQ(suc(A_2), suc(B_18)))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~iLEQ(suc(A_2), suc(B_18)))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~iLEQ(suc(A_2), suc(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) | (~iLEQ(suc(A_2), suc(B_18)))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) | (~iLEQ(suc(A_2), suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> (((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))))), rewrite((((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18)))))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) | (~iLEQ(suc(A_2), suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(191,plain,
% 0.19/0.46 (![B_18: $i, A_2: $i, B_19: $i] : ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) | (~iLEQ(suc(A_2), suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2))))) <=> ![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[190])).
% 0.19/0.46 tff(192,axiom,(![B_18: $i, A_2: $i, B_19: $i] : ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_19))))) | (~iLEQ(suc(B_18), suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(A_2)))) | (~tptp_fun__E_(|'0'|, f(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19)))))) | (~tptp_fun__E_(f(B_18), f(suc(B_18))))) | (~tptp_fun__E_(|'0'|, f(B_18)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18))))) | (~tptp_fun__E_(f(B_19), f(suc(B_19))))) | (~iLEQ(suc(A_2), suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_204')).
% 0.19/0.47 tff(193,plain,
% 0.19/0.47 (![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.19/0.47 tff(194,plain,
% 0.19/0.47 (![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.19/0.47 tff(195,plain,(
% 0.19/0.47 ![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[194])).
% 0.19/0.47 tff(196,plain,
% 0.19/0.47 (![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.19/0.47 tff(197,plain,
% 0.19/0.47 (((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(198,plain,
% 0.19/0.47 (((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~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))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, 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(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(199,plain,
% 0.19/0.47 (((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | ((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~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))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))) <=> ((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[198])).
% 0.19/0.47 tff(200,plain,
% 0.19/0.47 (((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | ((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~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))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))) <=> ((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[199, 197])).
% 0.19/0.47 tff(201,plain,
% 0.19/0.47 ((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | ((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~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))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(202,plain,
% 0.19/0.47 ((~![B_18: $i, A_2: $i, B_19: $i] : ((~iLEQ(suc(B_18), suc(B_19))) | (~iLEQ(suc(A_2), suc(B_18))) | (~tptp_fun__E_(f(B_19), f(suc(B_19)))) | (~tptp_fun__E_(f(B_18), f(suc(B_18)))) | (~tptp_fun__E_(f(A_2), f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(B_18)))) | (~tptp_fun__E_(|'0'|, f(B_18))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_19))))) | (~tptp_fun__E_(|'0'|, f(B_19))) | (~tptp_fun__E_(|'0'|, f(A_2))) | (~tptp_fun__E_(|'0'|, f(suc(B_19)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_2))))) | (~tptp_fun__E_(|'0'|, f(suc(A_2)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_18))))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.19/0.47 tff(203,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[202, 196, 88, 112, 137, 169, 186])).
% 0.19/0.47 tff(204,plain,(tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.47 tff(205,assumption,(tptp_fun__E_(s(|'0'|), f(z))), introduced(assumption)).
% 0.19/0.47 tff(206,assumption,(tptp_fun__E_(s(|'0'|), f(suc(z)))), introduced(assumption)).
% 0.19/0.47 tff(207,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(z))))), introduced(assumption)).
% 0.19/0.47 tff(208,plain,
% 0.19/0.47 (^[A_1: $i] : refl((iLEQ(suc(A_1), 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(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)))) | (~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(A_1)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(209,plain,
% 0.19/0.47 (![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[208])).
% 0.19/0.47 tff(210,plain,
% 0.19/0.47 (![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(211,plain,
% 0.19/0.47 (^[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(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(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(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))))), rewrite((((~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_(f(A_1), f(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_(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_(f(A_1), f(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_(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_(f(A_1), f(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_(s(|'0'|), f(A_1)))))), rewrite((((~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(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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(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_(f(A_1), f(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_(s(|'0'|), f(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_(f(A_1), f(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_(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(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))) <=> (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(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_(f(A_1), f(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_(s(|'0'|), f(A_1))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(212,plain,
% 0.19/0.47 (![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_(f(A_1), f(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_(s(|'0'|), f(A_1))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[211])).
% 0.19/0.47 tff(213,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_25')).
% 0.19/0.47 tff(214,plain,
% 0.19/0.47 (![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.47 tff(215,plain,
% 0.19/0.47 (![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.19/0.47 tff(216,plain,(
% 0.19/0.47 ![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[215])).
% 0.19/0.47 tff(217,plain,
% 0.19/0.47 (![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[216, 209])).
% 0.19/0.47 tff(218,plain,
% 0.19/0.47 (((~![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(z), suc(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(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | iLEQ(suc(z), suc(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(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(219,plain,
% 0.19/0.47 ((~![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(z), suc(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(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(220,plain,
% 0.19/0.47 ((~![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | iLEQ(suc(z), suc(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(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.19/0.47 tff(221,plain,
% 0.19/0.47 (iLEQ(suc(z), suc(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(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[220, 217])).
% 0.19/0.47 tff(222,plain,
% 0.19/0.47 (~tptp_fun__E_(f(z), f(suc(z)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[221, 113, 206, 205, 207])).
% 0.19/0.47 tff(223,plain,
% 0.19/0.47 (^[A_1: $i] : refl((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)) | 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)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(224,plain,
% 0.19/0.47 (![A_1: $i] : (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)))) <=> ![A_1: $i] : (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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[223])).
% 0.19/0.47 tff(225,plain,
% 0.19/0.47 (![A_1: $i] : (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)))) <=> ![A_1: $i] : (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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(226,plain,
% 0.19/0.47 (^[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))) <=> (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))))), (((((~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))) <=> (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))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(227,plain,
% 0.19/0.47 (![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] : (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))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[226])).
% 0.19/0.47 tff(228,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_85')).
% 0.19/0.47 tff(229,plain,
% 0.19/0.47 (![A_1: $i] : (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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.19/0.47 tff(230,plain,
% 0.19/0.47 (![A_1: $i] : (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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[229, 225])).
% 0.19/0.47 tff(231,plain,(
% 0.19/0.47 ![A_1: $i] : (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))))),
% 0.19/0.47 inference(skolemize,[status(sab)],[230])).
% 0.19/0.47 tff(232,plain,
% 0.19/0.47 (![A_1: $i] : (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))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[231, 224])).
% 0.19/0.47 tff(233,plain,
% 0.19/0.47 (((~![A_1: $i] : (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(z), 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))))) <=> ((~![A_1: $i] : (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(z), 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))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(234,plain,
% 0.19/0.47 ((~![A_1: $i] : (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(z), 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))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(235,plain,
% 0.19/0.48 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.19/0.48 tff(236,plain,
% 0.19/0.48 (iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[235, 232])).
% 0.19/0.48 tff(237,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[236, 222, 113, 205, 206])).
% 0.19/0.48 tff(238,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,[]))).
% 0.19/0.48 tff(239,plain,
% 0.19/0.48 (iLEQ(suc(z), suc(z))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[238, 207, 206, 205])).
% 0.19/0.48 tff(240,plain,
% 0.19/0.48 (^[B_11: $i, A_1: $i, B_12: $i] : refl(((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(241,plain,
% 0.19/0.48 (![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> ![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[240])).
% 0.19/0.48 tff(242,plain,
% 0.19/0.48 (![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> ![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(243,plain,
% 0.19/0.48 (^[B_11: $i, A_1: $i, B_12: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~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(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~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(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) <=> (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~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(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~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(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) <=> ((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) <=> ((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> (((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~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(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~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(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) <=> (((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~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(B_11)))))))), rewrite((((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~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(B_11)))))) <=> ((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) <=> ((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) <=> (((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))))), rewrite((((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> (((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~iLEQ(suc(B_11), suc(B_12)))))), rewrite((((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1)))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(244,plain,
% 0.19/0.49 (![B_11: $i, A_1: $i, B_12: $i] : ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[243])).
% 0.19/0.49 tff(245,axiom,(![B_11: $i, A_1: $i, B_12: $i] : ((((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~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(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_8')).
% 0.19/0.49 tff(246,plain,
% 0.19/0.49 (![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.19/0.49 tff(247,plain,
% 0.19/0.49 (![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[246, 242])).
% 0.19/0.49 tff(248,plain,(
% 0.19/0.49 ![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[247])).
% 0.19/0.49 tff(249,plain,
% 0.19/0.49 (![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[248, 241])).
% 0.19/0.49 tff(250,plain,
% 0.19/0.49 (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(251,plain,
% 0.19/0.49 (((~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), 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(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(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(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(252,plain,
% 0.19/0.49 (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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))) | (~iLEQ(suc(z), 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(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | ((~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[251])).
% 0.19/0.49 tff(253,plain,
% 0.19/0.49 (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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))) | (~iLEQ(suc(z), 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(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[252, 250])).
% 0.19/0.49 tff(254,plain,
% 0.19/0.49 ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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))) | (~iLEQ(suc(z), 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(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(255,plain,
% 0.19/0.49 ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.19/0.49 tff(256,plain,
% 0.19/0.49 (~tptp_fun__E_(f(z), f(suc(z)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[255, 249, 205, 207, 206, 239])).
% 0.19/0.49 tff(257,plain,
% 0.19/0.49 (^[B_11: $i, A_1: $i, B_12: $i] : refl((tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) <=> (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(258,plain,
% 0.19/0.49 (![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) <=> ![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[257])).
% 0.19/0.49 tff(259,plain,
% 0.19/0.49 (![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) <=> ![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(260,plain,
% 0.19/0.49 (^[B_11: $i, A_1: $i, B_12: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) <=> ((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) <=> (((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), (((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) <=> ((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~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(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~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(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) <=> (((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), (((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) <=> ((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> (((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))))), rewrite((((~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> (((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~iLEQ(suc(B_11), suc(B_12)))))), rewrite((((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), (((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))))), rewrite((((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) <=> ((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | tptp_fun__E_(f(B_11), f(suc(B_11)))))), rewrite(((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) <=> (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) <=> (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) | tptp_fun__E_(f(B_12), f(suc(B_12)))) <=> ((tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | tptp_fun__E_(f(B_12), f(suc(B_12)))))), rewrite(((tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11))))) | tptp_fun__E_(f(B_12), f(suc(B_12)))) <=> (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))), ((((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) | tptp_fun__E_(f(B_12), f(suc(B_12)))) <=> (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(261,plain,
% 0.19/0.50 (![B_11: $i, A_1: $i, B_12: $i] : (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) | tptp_fun__E_(f(B_12), f(suc(B_12)))) <=> ![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[260])).
% 0.19/0.50 tff(262,axiom,(![B_11: $i, A_1: $i, B_12: $i] : (((((((((((~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(B_11)))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) | tptp_fun__E_(f(B_11), f(suc(B_11)))) | tptp_fun__E_(f(B_12), f(suc(B_12))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_106')).
% 0.19/0.50 tff(263,plain,
% 0.19/0.50 (![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.19/0.50 tff(264,plain,
% 0.19/0.50 (![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.19/0.50 tff(265,plain,(
% 0.19/0.50 ![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[264])).
% 0.19/0.50 tff(266,plain,
% 0.19/0.50 (![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.19/0.50 tff(267,plain,
% 0.19/0.50 (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(268,plain,
% 0.19/0.50 ((tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~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(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(269,plain,
% 0.19/0.50 (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[268])).
% 0.19/0.50 tff(270,plain,
% 0.19/0.50 (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[269, 267])).
% 0.19/0.50 tff(271,plain,
% 0.19/0.50 ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(272,plain,
% 0.19/0.50 ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.19/0.50 tff(273,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[272, 266, 205, 206, 239, 256])).
% 0.19/0.50 tff(274,plain,((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(275,plain,
% 0.19/0.50 ((~tptp_fun__E_(s(|'0'|), f(z))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[274, 204])).
% 0.19/0.50 tff(276,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[275, 46, 26])).
% 0.19/0.50 tff(277,plain,(tptp_fun__LE_(f(z), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.50 tff(278,plain,
% 0.19/0.50 (tptp_fun__E_(|'0'|, f(z))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[87, 277])).
% 0.19/0.50 tff(279,assumption,(~tptp_fun__LE_(f(suc(z)), s(|'0'|))), introduced(assumption)).
% 0.19/0.50 tff(280,plain,
% 0.19/0.50 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (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_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(281,plain,
% 0.19/0.50 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(282,plain,
% 0.19/0.50 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(B_10), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(B_10)))) | tptp_fun__LE_(f(suc(z)), s(|'0'|)) | (~tptp_fun__LE_(f(suc(z)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.19/0.50 tff(283,plain,
% 0.19/0.50 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[282, 20, 30])).
% 0.19/0.50 tff(284,plain,
% 0.19/0.50 (tptp_fun__E_(s(|'0'|), f(suc(z)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[283, 279])).
% 0.19/0.50 tff(285,assumption,(~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))), introduced(assumption)).
% 0.19/0.50 tff(286,plain,
% 0.19/0.50 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(287,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[286, 8, 285])).
% 0.19/0.51 tff(288,plain,(tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(289,plain,
% 0.19/0.51 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(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_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(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'|)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(290,plain,
% 0.19/0.51 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(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'|)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(291,plain,
% 0.19/0.51 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(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'|))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.19/0.51 tff(292,plain,
% 0.19/0.51 (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'|))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[291, 61])).
% 0.19/0.51 tff(293,plain,
% 0.19/0.51 (tptp_fun__LE_(f(suc(z)), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[292, 288])).
% 0.19/0.51 tff(294,plain,
% 0.19/0.51 (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[293, 279])).
% 0.19/0.51 tff(295,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))), introduced(assumption)).
% 0.19/0.51 tff(296,assumption,(~iLEQ(suc(suc(z)), suc(suc(z)))), introduced(assumption)).
% 0.19/0.51 tff(297,plain,
% 0.19/0.51 (((~![A_1: $i] : (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))))) | ((~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_(f(suc(z)), f(suc(suc(z)))))) <=> ((~![A_1: $i] : (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))))) | (~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_(f(suc(z)), f(suc(suc(z)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(298,plain,
% 0.19/0.51 ((iLEQ(suc(suc(z)), 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_(f(suc(z)), f(suc(suc(z)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(299,plain,
% 0.19/0.51 (((~![A_1: $i] : (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(suc(z)), 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)))))) <=> ((~![A_1: $i] : (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))))) | ((~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_(f(suc(z)), f(suc(suc(z))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[298])).
% 0.19/0.51 tff(300,plain,
% 0.19/0.51 (((~![A_1: $i] : (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(suc(z)), 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)))))) <=> ((~![A_1: $i] : (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))))) | (~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_(f(suc(z)), f(suc(suc(z)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[299, 297])).
% 0.19/0.51 tff(301,plain,
% 0.19/0.51 ((~![A_1: $i] : (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(suc(z)), 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)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(302,plain,
% 0.19/0.51 ((~![A_1: $i] : (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))))) | (~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_(f(suc(z)), f(suc(suc(z))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.19/0.51 tff(303,plain,
% 0.19/0.51 ((~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_(f(suc(z)), f(suc(suc(z))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[302, 232])).
% 0.19/0.51 tff(304,plain,
% 0.19/0.51 (tptp_fun__E_(f(suc(z)), f(suc(suc(z))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[303, 296, 207, 206])).
% 0.19/0.51 tff(305,plain,
% 0.19/0.51 (((~![A_1: $i] : (iLEQ(suc(A_1), 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(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)))) | iLEQ(suc(suc(z)), suc(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_(f(A_1), f(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_(s(|'0'|), f(A_1))))) | (~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_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(306,plain,
% 0.19/0.51 ((iLEQ(suc(suc(z)), suc(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_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(307,plain,
% 0.19/0.51 (((~![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(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)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), 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(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)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[306])).
% 0.19/0.51 tff(308,plain,
% 0.19/0.51 (((~![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(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)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), 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(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)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[307, 305])).
% 0.19/0.51 tff(309,plain,
% 0.19/0.51 ((~![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(z)), suc(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)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(310,plain,
% 0.19/0.51 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.19/0.51 tff(311,plain,
% 0.19/0.51 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | iLEQ(suc(suc(z)), suc(suc(z))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[310, 217])).
% 0.19/0.51 tff(312,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[311, 304, 296, 207, 206, 295])).
% 0.19/0.51 tff(313,plain,(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(suc(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.51 tff(314,plain,
% 0.19/0.51 (iLEQ(suc(suc(z)), suc(suc(z)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[313, 295, 206, 207])).
% 0.19/0.51 tff(315,plain,
% 0.19/0.51 (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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)))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(316,plain,
% 0.19/0.51 (((~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(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(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(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)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(317,plain,
% 0.19/0.51 (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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)))) | (~iLEQ(suc(suc(z)), 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(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[316])).
% 0.19/0.51 tff(318,plain,
% 0.19/0.51 (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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)))) | (~iLEQ(suc(suc(z)), 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(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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)))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[317, 315])).
% 0.19/0.51 tff(319,plain,
% 0.19/0.51 ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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)))) | (~iLEQ(suc(suc(z)), 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(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(320,plain,
% 0.19/0.51 ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.19/0.51 tff(321,plain,
% 0.19/0.51 (~tptp_fun__E_(f(suc(z)), f(suc(suc(z))))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[320, 249, 207, 206, 295, 314])).
% 0.19/0.51 tff(322,plain,
% 0.19/0.51 (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | ((~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)))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (~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)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(323,plain,
% 0.19/0.51 ((tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(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(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(324,plain,
% 0.19/0.51 (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | ((~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))))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[323])).
% 0.19/0.51 tff(325,plain,
% 0.19/0.51 (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (~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)))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[324, 322])).
% 0.19/0.52 tff(326,plain,
% 0.19/0.52 ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(327,plain,
% 0.19/0.52 ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z)))) | tptp_fun__E_(f(suc(z)), f(suc(suc(z)))) | (~iLEQ(suc(suc(z)), suc(suc(z))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.19/0.52 tff(328,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[327, 266, 207, 206, 314, 321])).
% 0.19/0.52 tff(329,plain,((~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))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(330,plain,
% 0.19/0.52 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(z))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[329, 204])).
% 0.19/0.52 tff(331,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[330, 294, 284])).
% 0.19/0.52 tff(332,plain,(tptp_fun__LE_(f(suc(z)), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(333,plain,
% 0.19/0.52 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[111, 332])).
% 0.19/0.52 tff(334,assumption,(tptp_fun__E_(|'0'|, f(suc(z)))), introduced(assumption)).
% 0.19/0.52 tff(335,plain,
% 0.19/0.52 (tptp_fun__E_(f(z), f(suc(z)))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[151, 114, 113, 334])).
% 0.19/0.52 tff(336,assumption,(~tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))), introduced(assumption)).
% 0.19/0.52 tff(337,plain,
% 0.19/0.52 ((~![A: $i] : tptp_fun__LE_(f(A), s(s(|'0'|)))) | tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(338,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[337, 8, 336])).
% 0.19/0.52 tff(339,plain,(tptp_fun__LE_(f(suc(suc(suc(suc(z))))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(340,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))), introduced(assumption)).
% 0.19/0.52 tff(341,plain,
% 0.19/0.52 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(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_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(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'|)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(342,plain,
% 0.19/0.52 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(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'|)))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(343,plain,
% 0.19/0.52 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(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'|))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.19/0.52 tff(344,plain,
% 0.19/0.52 (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'|))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[343, 61])).
% 0.19/0.52 tff(345,plain,
% 0.19/0.52 (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[344, 340, 339])).
% 0.19/0.52 tff(346,plain,
% 0.19/0.52 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (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_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | 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'|)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(347,plain,
% 0.19/0.52 ((tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) <=> (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'|)))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(348,plain,
% 0.19/0.52 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (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'|))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[347])).
% 0.19/0.52 tff(349,plain,
% 0.19/0.52 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | 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'|)))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[348, 346])).
% 0.19/0.52 tff(350,plain,
% 0.19/0.52 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | (tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)) | (~tptp_fun__LE_(f(suc(suc(suc(z)))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(351,plain,
% 0.19/0.52 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), s(|'0'|)) | (~tptp_fun__LE_(f(suc(B_10)), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(suc(B_10))))) | 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'|))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.19/0.52 tff(352,plain,
% 0.19/0.52 (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'|))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[351, 40])).
% 0.19/0.52 tff(353,plain,
% 0.19/0.52 (tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[352, 340, 288])).
% 0.19/0.52 tff(354,assumption,(tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))), introduced(assumption)).
% 0.19/0.52 tff(355,assumption,(~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))), introduced(assumption)).
% 0.19/0.52 tff(356,plain,
% 0.19/0.52 (((~![A_1: $i] : (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))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))))) <=> ((~![A_1: $i] : (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))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(357,plain,
% 0.19/0.52 ((iLEQ(suc(suc(suc(z))), 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(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(358,plain,
% 0.19/0.52 (((~![A_1: $i] : (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(suc(suc(z))), 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))))))) <=> ((~![A_1: $i] : (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))))) | ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[357])).
% 0.19/0.52 tff(359,plain,
% 0.19/0.52 (((~![A_1: $i] : (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(suc(suc(z))), 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))))))) <=> ((~![A_1: $i] : (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))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[358, 356])).
% 0.19/0.52 tff(360,plain,
% 0.19/0.52 ((~![A_1: $i] : (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(suc(suc(z))), 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))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(361,plain,
% 0.19/0.52 ((~![A_1: $i] : (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))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.19/0.52 tff(362,plain,
% 0.19/0.52 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[361, 232])).
% 0.19/0.52 tff(363,plain,
% 0.19/0.52 (tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[362, 355, 204, 295])).
% 0.19/0.52 tff(364,plain,
% 0.19/0.52 (((~![A_1: $i] : (iLEQ(suc(A_1), 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(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_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), 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(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_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(365,plain,
% 0.19/0.52 ((iLEQ(suc(suc(suc(z))), 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(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_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(366,plain,
% 0.19/0.52 (((~![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(suc(z))), 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(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), 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(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_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[365])).
% 0.19/0.52 tff(367,plain,
% 0.19/0.52 (((~![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(suc(z))), 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(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), 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(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_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[366, 364])).
% 0.19/0.52 tff(368,plain,
% 0.19/0.52 ((~![A_1: $i] : (iLEQ(suc(A_1), 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(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (iLEQ(suc(suc(suc(z))), 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(suc(z))))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(369,plain,
% 0.19/0.52 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.19/0.52 tff(370,plain,
% 0.19/0.52 ((~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(suc(z))))))) | iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))) | (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[369, 217])).
% 0.19/0.52 tff(371,plain,
% 0.19/0.52 ($false),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[370, 363, 355, 204, 295, 354])).
% 0.19/0.52 tff(372,plain,(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(suc(suc(z)))))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.52 tff(373,plain,
% 0.19/0.52 (iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[372, 353, 345])).
% 0.19/0.52 tff(374,plain,
% 0.19/0.52 (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(375,plain,
% 0.19/0.53 (((~iLEQ(suc(suc(suc(z))), suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), 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(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)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(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(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))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(376,plain,
% 0.19/0.53 (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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))))) | (~iLEQ(suc(suc(suc(z))), 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(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)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(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(suc(z))))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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)))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[375])).
% 0.19/0.53 tff(377,plain,
% 0.19/0.53 (((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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))))) | (~iLEQ(suc(suc(suc(z))), 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(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)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(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(suc(z))))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[376, 374])).
% 0.19/0.53 tff(378,plain,
% 0.19/0.53 ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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))))) | (~iLEQ(suc(suc(suc(z))), 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(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)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(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(suc(z))))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(379,plain,
% 0.19/0.53 ((~![B_11: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_12))))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(B_11))))) | (~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)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[378, 377])).
% 0.19/0.53 tff(380,plain,
% 0.19/0.53 (~tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z)))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[379, 249, 204, 353, 345, 373])).
% 0.19/0.53 tff(381,plain,
% 0.19/0.53 (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | ((~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))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (~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))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(382,plain,
% 0.19/0.53 ((tptp_fun__E_(f(suc(suc(z))), 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))))) | (~iLEQ(suc(suc(suc(z))), 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(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_(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))))))),
% 0.19/0.53 inference(rewrite,[status(thm)],[])).
% 0.19/0.53 tff(383,plain,
% 0.19/0.53 (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(suc(z))), 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))))) | (~iLEQ(suc(suc(suc(z))), 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(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)))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | ((~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)))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[382])).
% 0.19/0.53 tff(384,plain,
% 0.19/0.53 (((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(suc(z))), 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))))) | (~iLEQ(suc(suc(suc(z))), 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(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)))))))) <=> ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (~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))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[383, 381])).
% 0.19/0.53 tff(385,plain,
% 0.19/0.53 ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (tptp_fun__E_(f(suc(suc(z))), 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))))) | (~iLEQ(suc(suc(suc(z))), 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(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)))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(386,plain,
% 0.19/0.53 ((~![B_11: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(s(|'0'|), f(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(A_1)))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_12)))) | (~tptp_fun__E_(s(|'0'|), f(A_1))) | (~tptp_fun__E_(s(|'0'|), f(B_12))) | (~tptp_fun__E_(s(|'0'|), f(suc(B_11)))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(z))))) | (~tptp_fun__E_(s(|'0'|), f(suc(suc(suc(z)))))) | tptp_fun__E_(f(suc(suc(z))), f(suc(suc(suc(z))))) | (~iLEQ(suc(suc(suc(z))), suc(suc(suc(z)))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.19/0.53 tff(387,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[386, 266, 204, 353, 373, 380])).
% 0.19/0.53 tff(388,plain,(tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(389,plain,
% 0.19/0.53 (tptp_fun__E_(|'0'|, f(suc(suc(z))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[136, 388])).
% 0.19/0.53 tff(390,plain,
% 0.19/0.53 (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[166, 389])).
% 0.19/0.53 tff(391,plain,
% 0.19/0.53 ($false),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[390, 335, 114, 113, 334])).
% 0.19/0.53 tff(392,plain,((~tptp_fun__E_(|'0'|, f(z))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(suc(z))))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.53 tff(393,plain,
% 0.19/0.53 (iLEQ(suc(z), suc(z))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[392, 333, 278])).
% 0.19/0.54 tff(394,plain,
% 0.19/0.54 (tptp_fun__E_(f(z), f(suc(z)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[185, 179, 278, 333, 393])).
% 0.19/0.54 tff(395,plain,
% 0.19/0.54 ($false),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[202, 196, 278, 333, 389, 393, 394])).
% 0.19/0.54 % SZS output end Proof
% 0.19/0.54 % E exiting
%------------------------------------------------------------------------------