%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO652-1 : 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 05:42:02 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SYO652-1 : TPTP v9.0.0. Released v7.3.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 13:21:10 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(tptp_fun__E__type, type, (
% 0.20/0.40 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.20/0.40 tff(f_type, type, (
% 0.20/0.40 f: $i > $i)).
% 0.20/0.40 tff(suc_type, type, (
% 0.20/0.40 suc: $i > $i)).
% 0.20/0.40 tff(z_type, type, (
% 0.20/0.40 z: $i)).
% 0.20/0.40 tff(iLEQ_type, type, (
% 0.20/0.40 iLEQ: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun__0__type, type, (
% 0.20/0.40 tptp_fun__0_: $i)).
% 0.20/0.40 tff(tptp_fun__LE__type, type, (
% 0.20/0.40 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.20/0.40 tff(s_type, type, (
% 0.20/0.40 s: $i > $i)).
% 0.20/0.40 tff(1,assumption,(~tptp_fun__LE_(f(suc(z)), s(|'0'|))), introduced(assumption)).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (^[A: $i] : refl(tptp_fun__LE_(f(A), s(|'0'|)) <=> tptp_fun__LE_(f(A), s(|'0'|)))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (![A: $i] : tptp_fun__LE_(f(A), s(|'0'|)) <=> ![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 (![A: $i] : tptp_fun__LE_(f(A), s(|'0'|)) <=> ![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(5,axiom,(![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_199')).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 (![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.40 tff(7,plain,(
% 0.20/0.40 ![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))),
% 0.20/0.40 inference(skolemize,[status(sab)],[6])).
% 0.20/0.40 tff(8,plain,
% 0.20/0.40 (![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 ((~![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))) | tptp_fun__LE_(f(suc(z)), s(|'0'|))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 ($false),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.40 tff(11,plain,(tptp_fun__LE_(f(suc(z)), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 ((~tptp_fun__LE_(f(z), |'0'|)) <=> (~tptp_fun__LE_(f(z), |'0'|))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(13,axiom,(~tptp_fun__LE_(f(z), |'0'|)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_99')).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (~tptp_fun__LE_(f(z), |'0'|)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (^[B_10: $i] : refl((tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))) <=> (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (^[B_10: $i] : rewrite((((~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))) | tptp_fun__LE_(f(B_10), |'0'|)) <=> (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (![B_10: $i] : (((~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))) | tptp_fun__LE_(f(B_10), |'0'|)) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.40 tff(20,axiom,(![B_10: $i] : (((~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10)))) | tptp_fun__LE_(f(B_10), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_191')).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.20/0.40 tff(23,plain,(
% 0.20/0.40 ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[22])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | (~tptp_fun__LE_(f(suc(B_10)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(B_10))))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 ((~tptp_fun__LE_(f(suc(z)), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (tptp_fun__E_(|'0'|, f(suc(z)))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[28, 11])).
% 0.20/0.40 tff(30,assumption,(~iLEQ(suc(z), suc(z))), introduced(assumption)).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 ((~![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))) | tptp_fun__LE_(f(z), s(|'0'|))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(32,plain,
% 0.20/0.40 (tptp_fun__LE_(f(z), s(|'0'|))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[31, 8])).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (^[B_10: $i] : refl(((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10))) <=> ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(34,plain,
% 0.20/0.40 (![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10))) <=> ![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10))) <=> ![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (^[B_10: $i] : rewrite((((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_10))) | tptp_fun__LE_(f(B_10), |'0'|)) <=> ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (![B_10: $i] : (((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_10))) | tptp_fun__LE_(f(B_10), |'0'|)) <=> ![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.40 tff(38,axiom,(![B_10: $i] : (((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__E_(|'0'|, f(B_10))) | tptp_fun__LE_(f(B_10), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_17')).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 (![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.41 tff(40,plain,
% 0.20/0.41 (![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.20/0.41 tff(41,plain,(
% 0.20/0.41 ![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.20/0.41 inference(skolemize,[status(sab)],[40])).
% 0.20/0.41 tff(42,plain,
% 0.20/0.41 (![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.20/0.41 tff(43,plain,
% 0.20/0.41 (((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(44,plain,
% 0.20/0.41 (((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z))) <=> (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(45,plain,
% 0.20/0.41 (((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | (tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[44])).
% 0.20/0.41 tff(46,plain,
% 0.20/0.41 (((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))) <=> ((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z)))),
% 0.20/0.41 inference(transitivity,[status(thm)],[45, 43])).
% 0.20/0.41 tff(47,plain,
% 0.20/0.41 ((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__LE_(f(z), |'0'|) | tptp_fun__E_(|'0'|, f(z)))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(48,plain,
% 0.20/0.41 ((~![B_10: $i] : ((~tptp_fun__LE_(f(B_10), s(|'0'|))) | tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(B_10)))) | tptp_fun__LE_(f(z), |'0'|) | (~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.20/0.41 tff(49,plain,
% 0.20/0.41 ((~tptp_fun__LE_(f(z), s(|'0'|))) | tptp_fun__E_(|'0'|, f(z))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[48, 42, 14])).
% 0.20/0.41 tff(50,plain,
% 0.20/0.41 (tptp_fun__E_(|'0'|, f(z))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[49, 32])).
% 0.20/0.41 tff(51,plain,
% 0.20/0.41 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(52,plain,
% 0.20/0.41 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.41 tff(53,plain,
% 0.20/0.41 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (^[A_1: $i] : trans(monotonicity(rewrite((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))), (((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'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_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))), (((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'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_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (![A_1: $i] : ((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'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_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.41 tff(56,axiom,(![A_1: $i] : ((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'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_44')).
% 0.20/0.41 tff(57,plain,
% 0.20/0.41 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.20/0.41 tff(59,plain,(
% 0.20/0.41 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[58])).
% 0.20/0.41 tff(60,plain,
% 0.20/0.41 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[59, 52])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 ((iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z)))))),
% 0.20/0.41 inference(monotonicity,[status(thm)],[62])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[63, 61])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | tptp_fun__E_(f(A_1), f(suc(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 ((~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | tptp_fun__E_(f(z), f(suc(z)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[66, 60, 50])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (tptp_fun__E_(f(z), f(suc(z)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[67, 30, 29])).
% 0.20/0.41 tff(69,assumption,(~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))), introduced(assumption)).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 ((~![A: $i] : tptp_fun__LE_(f(A), s(|'0'|))) | tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 ($false),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[70, 8, 69])).
% 0.20/0.41 tff(72,plain,(tptp_fun__LE_(f(suc(suc(z))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (^[B_10: $i] : refl((tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|)))) <=> (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|)))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|)))) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (^[B_10: $i] : rewrite((((~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_10))))) | tptp_fun__LE_(f(B_10), |'0'|)) <=> (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|)))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (![B_10: $i] : (((~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_10))))) | tptp_fun__LE_(f(B_10), |'0'|)) <=> ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[76])).
% 0.20/0.41 tff(78,axiom,(![B_10: $i] : (((~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(suc(suc(B_10))))) | tptp_fun__LE_(f(B_10), |'0'|))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.20/0.42 tff(79,plain,
% 0.20/0.42 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.42 tff(80,plain,
% 0.20/0.42 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.20/0.42 tff(81,plain,(
% 0.20/0.42 ![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[80])).
% 0.20/0.42 tff(82,plain,
% 0.20/0.42 (![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), s(|'0'|))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.20/0.42 tff(83,plain,
% 0.20/0.42 (((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), 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_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), 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'|))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(84,plain,
% 0.20/0.42 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), 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'|))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(85,plain,
% 0.20/0.42 ((~![B_10: $i] : (tptp_fun__LE_(f(B_10), |'0'|) | tptp_fun__E_(|'0'|, f(suc(suc(B_10)))) | (~tptp_fun__LE_(f(suc(suc(B_10))), 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'|)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.42 tff(86,plain,
% 0.20/0.42 (tptp_fun__E_(|'0'|, f(suc(suc(z)))) | (~tptp_fun__LE_(f(suc(suc(z))), s(|'0'|)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[85, 82, 14])).
% 0.20/0.42 tff(87,plain,
% 0.20/0.42 (tptp_fun__E_(|'0'|, f(suc(suc(z))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[86, 72])).
% 0.20/0.42 tff(88,plain,
% 0.20/0.42 (^[A_1: $i] : refl((iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(89,plain,
% 0.20/0.42 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.42 tff(90,plain,
% 0.20/0.42 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(91,plain,
% 0.20/0.42 (^[A_1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))), ((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))), ((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))))), (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))), (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))), ((((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(92,plain,
% 0.20/0.42 (![A_1: $i] : (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | iLEQ(suc(A_1), suc(A_1))) <=> ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[91])).
% 0.20/0.42 tff(93,axiom,(![A_1: $i] : (((((~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | iLEQ(suc(A_1), suc(A_1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_149')).
% 0.20/0.42 tff(94,plain,
% 0.20/0.42 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.20/0.42 tff(95,plain,
% 0.20/0.42 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.20/0.42 tff(96,plain,(
% 0.20/0.42 ![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[95])).
% 0.20/0.42 tff(97,plain,
% 0.20/0.42 (![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.20/0.42 tff(98,plain,
% 0.20/0.42 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(99,plain,
% 0.20/0.42 ((iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(100,plain,
% 0.20/0.42 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(f(z), f(suc(z))))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[99])).
% 0.20/0.42 tff(101,plain,
% 0.20/0.42 (((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[100, 98])).
% 0.20/0.42 tff(102,plain,
% 0.20/0.42 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(103,plain,
% 0.20/0.42 ((~![A_1: $i] : (iLEQ(suc(A_1), suc(A_1)) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(f(z), f(suc(z))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.20/0.42 tff(104,plain,
% 0.20/0.42 ((~tptp_fun__E_(|'0'|, f(suc(z)))) | iLEQ(suc(z), suc(z)) | (~tptp_fun__E_(f(z), f(suc(z))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[103, 97, 87, 50])).
% 0.20/0.42 tff(105,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[104, 68, 30, 29])).
% 0.20/0.42 tff(106,plain,(iLEQ(suc(z), suc(z))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(107,plain,
% 0.20/0.42 (^[B_11: $i, B_13: $i, A_1: $i, B_12: $i] : refl(((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(108,plain,
% 0.20/0.42 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) <=> ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.42 tff(109,plain,
% 0.20/0.42 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) <=> ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(110,plain,
% 0.20/0.43 (^[B_11: $i, B_13: $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(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) <=> ((~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) <=> (((~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))))), rewrite((((~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) <=> ((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) <=> ((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> (((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(A_1)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) <=> (((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_13)))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_13)))) <=> ((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) <=> ((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) <=> (((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'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_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(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_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) <=> (((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))))), rewrite((((~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(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_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(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_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(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_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> (((~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~iLEQ(suc(A_1), suc(B_11)))))), rewrite((((~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~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_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) <=> (((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))))), rewrite((((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_12)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) <=> ((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) <=> ((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) <=> (((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), (((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) <=> (((~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) <=> ((~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), (((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) <=> ((~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))))), ((((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> (((~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~iLEQ(suc(B_11), suc(B_12)))))), rewrite((((~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))), ((((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(111,plain,
% 0.20/0.45 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[110])).
% 0.20/0.45 tff(112,axiom,(![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (((((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1)))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12))))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12)))))) | (~tptp_fun__E_(f(A_1), f(suc(A_1))))) | (~tptp_fun__E_(f(B_11), f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13)))))) | (~tptp_fun__E_(f(B_13), f(suc(B_13))))) | (~iLEQ(suc(B_11), suc(B_12))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_96')).
% 0.20/0.45 tff(113,plain,
% 0.20/0.45 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.45 tff(114,plain,
% 0.20/0.45 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.20/0.45 tff(115,plain,(
% 0.20/0.45 ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[114])).
% 0.20/0.45 tff(116,plain,
% 0.20/0.45 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.20/0.45 tff(117,plain,
% 0.20/0.45 (((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(118,plain,
% 0.20/0.46 (((~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)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(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(suc(z))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z)))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(119,plain,
% 0.20/0.46 (((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | ((~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)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(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(suc(z))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))) <=> ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~iLEQ(suc(z), suc(z)))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[118])).
% 0.20/0.46 tff(120,plain,
% 0.20/0.46 (((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | ((~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)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(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(suc(z))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))) <=> ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[119, 117])).
% 0.20/0.46 tff(121,plain,
% 0.20/0.46 ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | ((~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)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(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(suc(z))))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(122,plain,
% 0.20/0.46 ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(f(B_13), f(suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(f(B_11), f(suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_12))))) | (~tptp_fun__E_(f(B_12), f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(B_11))))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~tptp_fun__E_(f(A_1), f(suc(A_1)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(A_1))))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(suc(suc(z))))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(f(z), f(suc(z)))) | (~iLEQ(suc(z), suc(z)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.46 tff(123,plain,
% 0.20/0.46 (~tptp_fun__E_(f(z), f(suc(z)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[122, 116, 87, 50, 29, 106])).
% 0.20/0.46 tff(124,plain,
% 0.20/0.46 (^[B_11: $i, B_13: $i, A_1: $i, B_12: $i] : refl((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(125,plain,
% 0.20/0.46 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) <=> ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.46 tff(126,plain,
% 0.20/0.46 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) <=> ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(127,plain,
% 0.20/0.46 (^[B_11: $i, B_13: $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(trans(monotonicity(rewrite(((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) <=> ((~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> (((~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))))), rewrite((((~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(B_11)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) <=> ((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) <=> ((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> (((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(A_1)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) <=> ((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) <=> (((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(B_13)))))), rewrite((((~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(B_13)))) <=> ((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) <=> ((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) <=> (((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) <=> ((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) <=> (((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))))), rewrite((((~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) <=> (((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(B_12)))))), rewrite((((~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) <=> ((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) <=> ((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> (((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~iLEQ(suc(B_11), suc(B_12)))))), rewrite((((~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~iLEQ(suc(B_11), suc(B_12)))) <=> ((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~iLEQ(suc(B_11), suc(B_12)))) | tptp_fun__E_(f(A_1), f(suc(A_1)))) <=> (((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | tptp_fun__E_(f(A_1), f(suc(A_1)))))), rewrite((((~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'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))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'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))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'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))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | tptp_fun__E_(f(B_12), f(suc(B_12)))))), rewrite(((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | tptp_fun__E_(f(B_12), f(suc(B_12)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))))), ((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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_13), f(suc(B_13)))) <=> ((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | tptp_fun__E_(f(B_13), f(suc(B_13)))))), rewrite(((tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11))))) | tptp_fun__E_(f(B_13), f(suc(B_13)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))), ((((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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_13), f(suc(B_13)))) <=> (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(128,plain,
% 0.20/0.47 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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_13), f(suc(B_13)))) <=> ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.47 tff(129,axiom,(![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (((((((((((((((~tptp_fun__E_(|'0'|, f(suc(B_11)))) | (~iLEQ(suc(B_12), suc(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(A_1))))) | (~tptp_fun__E_(|'0'|, f(B_11)))) | (~tptp_fun__E_(|'0'|, f(A_1)))) | (~tptp_fun__E_(|'0'|, f(B_13)))) | (~tptp_fun__E_(|'0'|, f(suc(B_12))))) | (~iLEQ(suc(A_1), suc(B_11)))) | (~tptp_fun__E_(|'0'|, f(suc(B_13))))) | (~tptp_fun__E_(|'0'|, f(B_12)))) | (~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_13), f(suc(B_13))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_16')).
% 0.20/0.47 tff(130,plain,
% 0.20/0.47 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.20/0.48 tff(132,plain,(
% 0.20/0.48 ![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[131])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 (![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 (((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))))) <=> ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 ((tptp_fun__E_(f(z), f(suc(z))) | (~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)))) | (~iLEQ(suc(z), 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(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z))))) <=> ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | (~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)))) | (~iLEQ(suc(z), 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(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | ((~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[135])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 (((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | (~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)))) | (~iLEQ(suc(z), 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(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))) <=> ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[136, 134])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | (tptp_fun__E_(f(z), f(suc(z))) | (~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)))) | (~iLEQ(suc(z), 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(z))) | (~tptp_fun__E_(|'0'|, f(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~iLEQ(suc(z), suc(z))) | (~tptp_fun__E_(|'0'|, f(suc(z)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 ((~![B_11: $i, B_13: $i, A_1: $i, B_12: $i] : (tptp_fun__E_(f(A_1), f(suc(A_1))) | (~iLEQ(suc(B_11), suc(B_12))) | tptp_fun__E_(f(B_13), f(suc(B_13))) | (~tptp_fun__E_(|'0'|, f(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_13)))) | (~iLEQ(suc(A_1), suc(B_11))) | tptp_fun__E_(f(B_11), f(suc(B_11))) | tptp_fun__E_(f(B_12), f(suc(B_12))) | (~tptp_fun__E_(|'0'|, f(suc(B_12)))) | (~tptp_fun__E_(|'0'|, f(B_13))) | (~tptp_fun__E_(|'0'|, f(A_1))) | (~tptp_fun__E_(|'0'|, f(B_11))) | (~tptp_fun__E_(|'0'|, f(suc(A_1)))) | (~iLEQ(suc(B_12), suc(B_13))) | (~tptp_fun__E_(|'0'|, f(suc(B_11)))))) | (~tptp_fun__E_(|'0'|, f(suc(z)))) | (~tptp_fun__E_(|'0'|, f(z))) | tptp_fun__E_(f(z), f(suc(z))) | (~iLEQ(suc(z), suc(z)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[139, 133, 50, 29, 106, 123])).
% 0.20/0.48 % SZS output end Proof
% 0.20/0.48 % E exiting
%------------------------------------------------------------------------------