%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYO631-1 : TPTP v9.0.0. Released v7.1.0.
% 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 05:41:59 AM UTC 2025
% Result : Unsatisfiable 0.99s 1.16s
% Output : Proof 1.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYO631-1 : TPTP v9.0.0. Released v7.1.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 13:20:40 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.99/1.16 % SZS status Unsatisfiable
% 0.99/1.16 % SZS output start Proof
% 0.99/1.16 tff(tptp_fun__LE__type, type, (
% 0.99/1.16 tptp_fun__LE_: ( $i * $i ) > $o)).
% 0.99/1.16 tff(s_type, type, (
% 0.99/1.16 s: $i > $i)).
% 0.99/1.16 tff(tptp_fun__0__type, type, (
% 0.99/1.16 tptp_fun__0_: $i)).
% 0.99/1.16 tff(f_type, type, (
% 0.99/1.16 f: $i > $i)).
% 0.99/1.16 tff(g_type, type, (
% 0.99/1.16 g: $i > $i)).
% 0.99/1.16 tff(elem_0_type, type, (
% 0.99/1.16 elem_0: $i)).
% 0.99/1.16 tff(tptp_fun__E__type, type, (
% 0.99/1.16 tptp_fun__E_: ( $i * $i ) > $o)).
% 0.99/1.16 tff(iLEQ_type, type, (
% 0.99/1.16 iLEQ: ( $i * $i ) > $o)).
% 0.99/1.16 tff(1,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 0.99/1.16 tff(2,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|)), introduced(assumption)).
% 0.99/1.16 tff(3,plain,
% 0.99/1.16 (^[A_30: $i] : refl((~tptp_fun__LE_(f(g(A_30)), |'0'|)) <=> (~tptp_fun__LE_(f(g(A_30)), |'0'|)))),
% 0.99/1.16 inference(bind,[status(th)],[])).
% 0.99/1.16 tff(4,plain,
% 0.99/1.16 (![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|)) <=> ![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))),
% 0.99/1.16 inference(quant_intro,[status(thm)],[3])).
% 0.99/1.16 tff(5,plain,
% 0.99/1.16 (![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|)) <=> ![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(6,axiom,(![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_36_51')).
% 0.99/1.16 tff(7,plain,
% 0.99/1.16 (![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.99/1.16 tff(8,plain,(
% 0.99/1.16 ![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))),
% 0.99/1.16 inference(skolemize,[status(sab)],[7])).
% 0.99/1.16 tff(9,plain,
% 0.99/1.16 (![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.99/1.16 tff(10,plain,
% 0.99/1.16 ((~![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(11,plain,
% 0.99/1.16 ($false),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[10, 9, 2])).
% 0.99/1.16 tff(12,plain,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|)), inference(lemma,lemma(discharge,[]))).
% 0.99/1.16 tff(13,assumption,(tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))), introduced(assumption)).
% 0.99/1.16 tff(14,plain,
% 0.99/1.16 (^[A_14: $i] : refl((~tptp_fun__E_(f(A_14), f(g(A_14)))) <=> (~tptp_fun__E_(f(A_14), f(g(A_14)))))),
% 0.99/1.16 inference(bind,[status(th)],[])).
% 0.99/1.16 tff(15,plain,
% 0.99/1.16 (![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14)))) <=> ![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))),
% 0.99/1.16 inference(quant_intro,[status(thm)],[14])).
% 0.99/1.16 tff(16,plain,
% 0.99/1.16 (![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14)))) <=> ![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(17,axiom,(![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_34_55')).
% 0.99/1.16 tff(18,plain,
% 0.99/1.16 (![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.99/1.16 tff(19,plain,(
% 0.99/1.16 ![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))),
% 0.99/1.16 inference(skolemize,[status(sab)],[18])).
% 0.99/1.16 tff(20,plain,
% 0.99/1.16 (![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.99/1.16 tff(21,plain,
% 0.99/1.16 ((~![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))) | (~tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(22,plain,
% 0.99/1.16 ($false),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[21, 20, 13])).
% 0.99/1.16 tff(23,plain,(~tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.16 tff(24,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|)), introduced(assumption)).
% 0.99/1.16 tff(25,assumption,(~tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))), introduced(assumption)).
% 0.99/1.16 tff(26,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))), introduced(assumption)).
% 0.99/1.16 tff(27,plain,
% 0.99/1.16 (^[A_14: $i] : refl(iLEQ(A_14, A_14) <=> iLEQ(A_14, A_14))),
% 0.99/1.16 inference(bind,[status(th)],[])).
% 0.99/1.16 tff(28,plain,
% 0.99/1.16 (![A_14: $i] : iLEQ(A_14, A_14) <=> ![A_14: $i] : iLEQ(A_14, A_14)),
% 0.99/1.16 inference(quant_intro,[status(thm)],[27])).
% 0.99/1.16 tff(29,plain,
% 0.99/1.16 (![A_14: $i] : iLEQ(A_14, A_14) <=> ![A_14: $i] : iLEQ(A_14, A_14)),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(30,axiom,(![A_14: $i] : iLEQ(A_14, A_14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_18_06')).
% 0.99/1.16 tff(31,plain,
% 0.99/1.16 (![A_14: $i] : iLEQ(A_14, A_14)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.99/1.16 tff(32,plain,(
% 0.99/1.16 ![A_14: $i] : iLEQ(A_14, A_14)),
% 0.99/1.16 inference(skolemize,[status(sab)],[31])).
% 0.99/1.16 tff(33,plain,
% 0.99/1.16 (![A_14: $i] : iLEQ(A_14, A_14)),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.99/1.16 tff(34,plain,
% 0.99/1.16 ((~![A_14: $i] : iLEQ(A_14, A_14)) | iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(35,plain,
% 0.99/1.16 (iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.99/1.16 tff(36,plain,
% 0.99/1.16 ((~![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(37,plain,
% 0.99/1.16 (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|)),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[36, 9])).
% 0.99/1.16 tff(38,assumption,(~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), introduced(assumption)).
% 0.99/1.16 tff(39,plain,
% 0.99/1.16 (^[B_18: $i, A_28: $i] : refl(((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|)))) <=> ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|)))))),
% 0.99/1.16 inference(bind,[status(th)],[])).
% 0.99/1.16 tff(40,plain,
% 0.99/1.16 (![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|)))) <=> ![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))),
% 0.99/1.16 inference(quant_intro,[status(thm)],[39])).
% 0.99/1.16 tff(41,plain,
% 0.99/1.16 (![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|)))) <=> ![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(42,plain,
% 0.99/1.16 (^[B_18: $i, A_28: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_28), s(|'0'|))) | (~iLEQ(A_28, B_18))) <=> ((~iLEQ(A_28, B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))), ((((~tptp_fun__LE_(f(A_28), s(|'0'|))) | (~iLEQ(A_28, B_18))) | tptp_fun__E_(|'0'|, f(B_18))) <=> (((~iLEQ(A_28, B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|)))) | tptp_fun__E_(|'0'|, f(B_18))))), rewrite((((~iLEQ(A_28, B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|)))) | tptp_fun__E_(|'0'|, f(B_18))) <=> ((~iLEQ(A_28, B_18)) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))), ((((~tptp_fun__LE_(f(A_28), s(|'0'|))) | (~iLEQ(A_28, B_18))) | tptp_fun__E_(|'0'|, f(B_18))) <=> ((~iLEQ(A_28, B_18)) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|)))))), (((((~tptp_fun__LE_(f(A_28), s(|'0'|))) | (~iLEQ(A_28, B_18))) | tptp_fun__E_(|'0'|, f(B_18))) | tptp_fun__LE_(f(B_18), |'0'|)) <=> (((~iLEQ(A_28, B_18)) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|)))) | tptp_fun__LE_(f(B_18), |'0'|)))), rewrite((((~iLEQ(A_28, B_18)) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|)))) | tptp_fun__LE_(f(B_18), |'0'|)) <=> ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))), (((((~tptp_fun__LE_(f(A_28), s(|'0'|))) | (~iLEQ(A_28, B_18))) | tptp_fun__E_(|'0'|, f(B_18))) | tptp_fun__LE_(f(B_18), |'0'|)) <=> ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))))),
% 0.99/1.16 inference(bind,[status(th)],[])).
% 0.99/1.16 tff(43,plain,
% 0.99/1.16 (![B_18: $i, A_28: $i] : ((((~tptp_fun__LE_(f(A_28), s(|'0'|))) | (~iLEQ(A_28, B_18))) | tptp_fun__E_(|'0'|, f(B_18))) | tptp_fun__LE_(f(B_18), |'0'|)) <=> ![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))),
% 0.99/1.16 inference(quant_intro,[status(thm)],[42])).
% 0.99/1.16 tff(44,axiom,(![B_18: $i, A_28: $i] : ((((~tptp_fun__LE_(f(A_28), s(|'0'|))) | (~iLEQ(A_28, B_18))) | tptp_fun__E_(|'0'|, f(B_18))) | tptp_fun__LE_(f(B_18), |'0'|))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_56_31')).
% 0.99/1.16 tff(45,plain,
% 0.99/1.16 (![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.99/1.16 tff(46,plain,
% 0.99/1.16 (![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.99/1.16 tff(47,plain,(
% 0.99/1.16 ![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))),
% 0.99/1.16 inference(skolemize,[status(sab)],[46])).
% 0.99/1.16 tff(48,plain,
% 0.99/1.16 (![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.99/1.16 tff(49,plain,
% 0.99/1.16 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(50,plain,
% 0.99/1.16 (((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(51,plain,
% 0.99/1.16 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[50])).
% 0.99/1.16 tff(52,plain,
% 0.99/1.16 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.16 inference(transitivity,[status(thm)],[51, 49])).
% 0.99/1.16 tff(53,plain,
% 0.99/1.16 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(54,plain,
% 0.99/1.16 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.99/1.16 tff(55,plain,
% 0.99/1.16 ($false),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[54, 48, 38, 37, 26, 35])).
% 0.99/1.16 tff(56,plain,(tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.16 tff(57,plain,
% 0.99/1.16 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.16 inference(unit_resolution,[status(thm)],[56, 26])).
% 0.99/1.16 tff(58,plain,
% 0.99/1.16 (^[A_30: $i] : refl((tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30)))) <=> (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30)))))),
% 0.99/1.16 inference(bind,[status(th)],[])).
% 0.99/1.16 tff(59,plain,
% 0.99/1.16 (![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30)))) <=> ![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))),
% 0.99/1.16 inference(quant_intro,[status(thm)],[58])).
% 0.99/1.16 tff(60,plain,
% 0.99/1.16 (![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30)))) <=> ![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(61,plain,
% 0.99/1.16 (^[A_30: $i] : rewrite((((~tptp_fun__E_(|'0'|, f(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30))))) | tptp_fun__E_(f(A_30), f(g(A_30)))) <=> (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30)))))),
% 0.99/1.16 inference(bind,[status(th)],[])).
% 0.99/1.16 tff(62,plain,
% 0.99/1.16 (![A_30: $i] : (((~tptp_fun__E_(|'0'|, f(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30))))) | tptp_fun__E_(f(A_30), f(g(A_30)))) <=> ![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))),
% 0.99/1.16 inference(quant_intro,[status(thm)],[61])).
% 0.99/1.16 tff(63,axiom,(![A_30: $i] : (((~tptp_fun__E_(|'0'|, f(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30))))) | tptp_fun__E_(f(A_30), f(g(A_30))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_2_25')).
% 0.99/1.16 tff(64,plain,
% 0.99/1.16 (![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.99/1.16 tff(65,plain,
% 0.99/1.16 (![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.99/1.16 tff(66,plain,(
% 0.99/1.16 ![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))),
% 0.99/1.16 inference(skolemize,[status(sab)],[65])).
% 0.99/1.16 tff(67,plain,
% 0.99/1.16 (![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))),
% 0.99/1.16 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.99/1.16 tff(68,plain,
% 0.99/1.16 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(69,plain,
% 0.99/1.16 ((tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.16 inference(rewrite,[status(thm)],[])).
% 0.99/1.16 tff(70,plain,
% 0.99/1.16 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.16 inference(monotonicity,[status(thm)],[69])).
% 0.99/1.16 tff(71,plain,
% 0.99/1.16 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.16 inference(transitivity,[status(thm)],[70, 68])).
% 0.99/1.16 tff(72,plain,
% 0.99/1.16 ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.16 inference(quant_inst,[status(thm)],[])).
% 0.99/1.16 tff(73,plain,
% 0.99/1.16 ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.99/1.17 tff(74,plain,
% 0.99/1.17 (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[73, 67, 57, 25])).
% 0.99/1.17 tff(75,plain,
% 0.99/1.17 (^[A_23: $i] : refl(iLEQ(A_23, g(A_23)) <=> iLEQ(A_23, g(A_23)))),
% 0.99/1.17 inference(bind,[status(th)],[])).
% 0.99/1.17 tff(76,plain,
% 0.99/1.17 (![A_23: $i] : iLEQ(A_23, g(A_23)) <=> ![A_23: $i] : iLEQ(A_23, g(A_23))),
% 0.99/1.17 inference(quant_intro,[status(thm)],[75])).
% 0.99/1.17 tff(77,plain,
% 0.99/1.17 (![A_23: $i] : iLEQ(A_23, g(A_23)) <=> ![A_23: $i] : iLEQ(A_23, g(A_23))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(78,axiom,(![A_23: $i] : iLEQ(A_23, g(A_23))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_3_02')).
% 0.99/1.17 tff(79,plain,
% 0.99/1.17 (![A_23: $i] : iLEQ(A_23, g(A_23))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.99/1.17 tff(80,plain,(
% 0.99/1.17 ![A_23: $i] : iLEQ(A_23, g(A_23))),
% 0.99/1.17 inference(skolemize,[status(sab)],[79])).
% 0.99/1.17 tff(81,plain,
% 0.99/1.17 (![A_23: $i] : iLEQ(A_23, g(A_23))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.99/1.17 tff(82,plain,
% 0.99/1.17 ((~![A_23: $i] : iLEQ(A_23, g(A_23))) | iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(83,plain,
% 0.99/1.17 (iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.99/1.17 tff(84,plain,
% 0.99/1.17 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(85,plain,
% 0.99/1.17 (((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(86,plain,
% 0.99/1.17 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|)))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[85])).
% 0.99/1.17 tff(87,plain,
% 0.99/1.17 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|))),
% 0.99/1.17 inference(transitivity,[status(thm)],[86, 84])).
% 0.99/1.17 tff(88,plain,
% 0.99/1.17 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(89,plain,
% 0.99/1.17 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|)),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.99/1.17 tff(90,plain,
% 0.99/1.17 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[89, 48, 26, 83])).
% 0.99/1.17 tff(91,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[90, 74, 24])).
% 0.99/1.17 tff(92,plain,(tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(93,plain,
% 0.99/1.17 (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[92, 23, 12])).
% 0.99/1.17 tff(94,assumption,(~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))), introduced(assumption)).
% 0.99/1.17 tff(95,plain,
% 0.99/1.17 (^[A_29: $i] : refl(iLEQ(A_29, A_29) <=> iLEQ(A_29, A_29))),
% 0.99/1.17 inference(bind,[status(th)],[])).
% 0.99/1.17 tff(96,plain,
% 0.99/1.17 (![A_29: $i] : iLEQ(A_29, A_29) <=> ![A_29: $i] : iLEQ(A_29, A_29)),
% 0.99/1.17 inference(quant_intro,[status(thm)],[95])).
% 0.99/1.17 tff(97,plain,
% 0.99/1.17 (![A_29: $i] : iLEQ(A_29, A_29) <=> ![A_29: $i] : iLEQ(A_29, A_29)),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(98,axiom,(![A_29: $i] : iLEQ(A_29, A_29)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_24_57')).
% 0.99/1.17 tff(99,plain,
% 0.99/1.17 (![A_29: $i] : iLEQ(A_29, A_29)),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.99/1.17 tff(100,plain,(
% 0.99/1.17 ![A_29: $i] : iLEQ(A_29, A_29)),
% 0.99/1.17 inference(skolemize,[status(sab)],[99])).
% 0.99/1.17 tff(101,plain,
% 0.99/1.17 (![A_29: $i] : iLEQ(A_29, A_29)),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.99/1.17 tff(102,plain,
% 0.99/1.17 ((~![A_29: $i] : iLEQ(A_29, A_29)) | iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(103,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[102, 101, 94])).
% 0.99/1.17 tff(104,plain,(iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(105,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))), introduced(assumption)).
% 0.99/1.17 tff(106,plain,
% 0.99/1.17 ((~![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(107,plain,
% 0.99/1.17 (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|)),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[106, 9])).
% 0.99/1.17 tff(108,plain,
% 0.99/1.17 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(109,plain,
% 0.99/1.17 (((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)))) <=> ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(110,plain,
% 0.99/1.17 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[109])).
% 0.99/1.17 tff(111,plain,
% 0.99/1.17 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))),
% 0.99/1.17 inference(transitivity,[status(thm)],[110, 108])).
% 0.99/1.17 tff(112,plain,
% 0.99/1.17 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(113,plain,
% 0.99/1.17 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.99/1.17 tff(114,plain,
% 0.99/1.17 ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[113, 48, 107])).
% 0.99/1.17 tff(115,plain,
% 0.99/1.17 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[114, 105, 104])).
% 0.99/1.17 tff(116,plain,
% 0.99/1.17 ((~![A_23: $i] : iLEQ(A_23, g(A_23))) | iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(117,plain,
% 0.99/1.17 (iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[116, 81])).
% 0.99/1.17 tff(118,plain,
% 0.99/1.17 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(119,plain,
% 0.99/1.17 (((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)))) <=> ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(120,plain,
% 0.99/1.17 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[119])).
% 0.99/1.17 tff(121,plain,
% 0.99/1.17 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))),
% 0.99/1.17 inference(transitivity,[status(thm)],[120, 118])).
% 0.99/1.17 tff(122,plain,
% 0.99/1.17 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(123,plain,
% 0.99/1.17 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.99/1.17 tff(124,plain,
% 0.99/1.17 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[123, 48, 117])).
% 0.99/1.17 tff(125,plain,
% 0.99/1.17 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[124, 105, 37])).
% 0.99/1.17 tff(126,plain,
% 0.99/1.17 ((~![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))) | (~tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(127,plain,
% 0.99/1.17 (~tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[126, 20])).
% 0.99/1.17 tff(128,plain,
% 0.99/1.17 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(129,plain,
% 0.99/1.17 ((tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(130,plain,
% 0.99/1.17 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.17 inference(monotonicity,[status(thm)],[129])).
% 0.99/1.17 tff(131,plain,
% 0.99/1.17 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.17 inference(transitivity,[status(thm)],[130, 128])).
% 0.99/1.17 tff(132,plain,
% 0.99/1.17 ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.17 inference(quant_inst,[status(thm)],[])).
% 0.99/1.17 tff(133,plain,
% 0.99/1.17 ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.99/1.17 tff(134,plain,
% 0.99/1.17 ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[133, 67, 127])).
% 0.99/1.17 tff(135,plain,
% 0.99/1.17 ($false),
% 0.99/1.17 inference(unit_resolution,[status(thm)],[134, 125, 115])).
% 0.99/1.17 tff(136,plain,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.17 tff(137,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))), introduced(assumption)).
% 0.99/1.17 tff(138,plain,
% 0.99/1.17 (^[B_16: $i, A_25: $i] : refl(((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|))))) <=> ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|))))))),
% 0.99/1.17 inference(bind,[status(th)],[])).
% 0.99/1.17 tff(139,plain,
% 0.99/1.17 (![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|))))) <=> ![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))),
% 0.99/1.17 inference(quant_intro,[status(thm)],[138])).
% 0.99/1.17 tff(140,plain,
% 0.99/1.17 (![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|))))) <=> ![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(141,plain,
% 0.99/1.17 (^[B_16: $i, A_25: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_25), s(s(|'0'|)))) | (~iLEQ(A_25, B_16))) <=> ((~iLEQ(A_25, B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))), ((((~tptp_fun__LE_(f(A_25), s(s(|'0'|)))) | (~iLEQ(A_25, B_16))) | tptp_fun__E_(s(|'0'|), f(B_16))) <=> (((~iLEQ(A_25, B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|))))) | tptp_fun__E_(s(|'0'|), f(B_16))))), rewrite((((~iLEQ(A_25, B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|))))) | tptp_fun__E_(s(|'0'|), f(B_16))) <=> ((~iLEQ(A_25, B_16)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))), ((((~tptp_fun__LE_(f(A_25), s(s(|'0'|)))) | (~iLEQ(A_25, B_16))) | tptp_fun__E_(s(|'0'|), f(B_16))) <=> ((~iLEQ(A_25, B_16)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|))))))), (((((~tptp_fun__LE_(f(A_25), s(s(|'0'|)))) | (~iLEQ(A_25, B_16))) | tptp_fun__E_(s(|'0'|), f(B_16))) | tptp_fun__LE_(f(B_16), s(|'0'|))) <=> (((~iLEQ(A_25, B_16)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|))))) | tptp_fun__LE_(f(B_16), s(|'0'|))))), rewrite((((~iLEQ(A_25, B_16)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|))))) | tptp_fun__LE_(f(B_16), s(|'0'|))) <=> ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))), (((((~tptp_fun__LE_(f(A_25), s(s(|'0'|)))) | (~iLEQ(A_25, B_16))) | tptp_fun__E_(s(|'0'|), f(B_16))) | tptp_fun__LE_(f(B_16), s(|'0'|))) <=> ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))))),
% 0.99/1.17 inference(bind,[status(th)],[])).
% 0.99/1.17 tff(142,plain,
% 0.99/1.17 (![B_16: $i, A_25: $i] : ((((~tptp_fun__LE_(f(A_25), s(s(|'0'|)))) | (~iLEQ(A_25, B_16))) | tptp_fun__E_(s(|'0'|), f(B_16))) | tptp_fun__LE_(f(B_16), s(|'0'|))) <=> ![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))),
% 0.99/1.17 inference(quant_intro,[status(thm)],[141])).
% 0.99/1.17 tff(143,axiom,(![B_16: $i, A_25: $i] : ((((~tptp_fun__LE_(f(A_25), s(s(|'0'|)))) | (~iLEQ(A_25, B_16))) | tptp_fun__E_(s(|'0'|), f(B_16))) | tptp_fun__LE_(f(B_16), s(|'0'|)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_23_21')).
% 0.99/1.17 tff(144,plain,
% 0.99/1.17 (![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.99/1.17 tff(145,plain,
% 0.99/1.17 (![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.99/1.17 tff(146,plain,(
% 0.99/1.17 ![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))),
% 0.99/1.17 inference(skolemize,[status(sab)],[145])).
% 0.99/1.17 tff(147,plain,
% 0.99/1.17 (![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))),
% 0.99/1.17 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.99/1.17 tff(148,plain,
% 0.99/1.17 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(149,plain,
% 0.99/1.17 (((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))))) <=> ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.17 inference(rewrite,[status(thm)],[])).
% 0.99/1.17 tff(150,plain,
% 0.99/1.17 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.18 inference(monotonicity,[status(thm)],[149])).
% 0.99/1.18 tff(151,plain,
% 0.99/1.18 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.18 inference(transitivity,[status(thm)],[150, 148])).
% 0.99/1.18 tff(152,plain,
% 0.99/1.18 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(153,plain,
% 0.99/1.18 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.99/1.18 tff(154,plain,
% 0.99/1.18 ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[153, 147, 104])).
% 0.99/1.18 tff(155,plain,
% 0.99/1.18 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[154, 137, 136])).
% 0.99/1.18 tff(156,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))), introduced(assumption)).
% 0.99/1.18 tff(157,plain,
% 0.99/1.18 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(158,plain,
% 0.99/1.18 (((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(159,plain,
% 0.99/1.18 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))))),
% 0.99/1.18 inference(monotonicity,[status(thm)],[158])).
% 0.99/1.18 tff(160,plain,
% 0.99/1.18 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)))),
% 0.99/1.18 inference(transitivity,[status(thm)],[159, 157])).
% 0.99/1.18 tff(161,plain,
% 0.99/1.18 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(162,plain,
% 0.99/1.18 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.99/1.18 tff(163,plain,
% 0.99/1.18 ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[162, 147, 117])).
% 0.99/1.18 tff(164,plain,
% 0.99/1.18 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[163, 137, 156])).
% 0.99/1.18 tff(165,plain,
% 0.99/1.18 (^[A_29: $i] : refl((tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29)))) <=> (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29)))))),
% 0.99/1.18 inference(bind,[status(th)],[])).
% 0.99/1.18 tff(166,plain,
% 0.99/1.18 (![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29)))) <=> ![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))),
% 0.99/1.18 inference(quant_intro,[status(thm)],[165])).
% 0.99/1.18 tff(167,plain,
% 0.99/1.18 (![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29)))) <=> ![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(168,plain,
% 0.99/1.18 (^[A_29: $i] : rewrite((((~tptp_fun__E_(s(|'0'|), f(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29))))) | tptp_fun__E_(f(A_29), f(g(A_29)))) <=> (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29)))))),
% 0.99/1.18 inference(bind,[status(th)],[])).
% 0.99/1.18 tff(169,plain,
% 0.99/1.18 (![A_29: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29))))) | tptp_fun__E_(f(A_29), f(g(A_29)))) <=> ![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))),
% 0.99/1.18 inference(quant_intro,[status(thm)],[168])).
% 0.99/1.18 tff(170,axiom,(![A_29: $i] : (((~tptp_fun__E_(s(|'0'|), f(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29))))) | tptp_fun__E_(f(A_29), f(g(A_29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_30_35')).
% 0.99/1.18 tff(171,plain,
% 0.99/1.18 (![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.99/1.18 tff(172,plain,
% 0.99/1.18 (![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.99/1.18 tff(173,plain,(
% 0.99/1.18 ![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))),
% 0.99/1.18 inference(skolemize,[status(sab)],[172])).
% 0.99/1.18 tff(174,plain,
% 0.99/1.18 (![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.99/1.18 tff(175,plain,
% 0.99/1.18 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(176,plain,
% 0.99/1.18 ((tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(177,plain,
% 0.99/1.18 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.18 inference(monotonicity,[status(thm)],[176])).
% 0.99/1.18 tff(178,plain,
% 0.99/1.18 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.18 inference(transitivity,[status(thm)],[177, 175])).
% 0.99/1.18 tff(179,plain,
% 0.99/1.18 ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(180,plain,
% 0.99/1.18 ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.99/1.18 tff(181,plain,
% 0.99/1.18 ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[180, 174, 127])).
% 0.99/1.18 tff(182,plain,
% 0.99/1.18 ($false),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[181, 164, 155])).
% 0.99/1.18 tff(183,plain,((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.18 tff(184,plain,
% 0.99/1.18 (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[183, 93])).
% 0.99/1.18 tff(185,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))), introduced(assumption)).
% 0.99/1.18 tff(186,plain,
% 0.99/1.18 ((~![A_23: $i] : iLEQ(A_23, g(A_23))) | iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(187,plain,
% 0.99/1.18 (iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[186, 81])).
% 0.99/1.18 tff(188,plain,
% 0.99/1.18 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(189,plain,
% 0.99/1.18 (((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)))) <=> (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(190,plain,
% 0.99/1.18 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|)))),
% 0.99/1.18 inference(monotonicity,[status(thm)],[189])).
% 0.99/1.18 tff(191,plain,
% 0.99/1.18 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|))),
% 0.99/1.18 inference(transitivity,[status(thm)],[190, 188])).
% 0.99/1.18 tff(192,plain,
% 0.99/1.18 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(193,plain,
% 0.99/1.18 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|)),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.99/1.18 tff(194,plain,
% 0.99/1.18 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), |'0'|)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[193, 48, 187])).
% 0.99/1.18 tff(195,plain,
% 0.99/1.18 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[194, 107])).
% 0.99/1.18 tff(196,plain,
% 0.99/1.18 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[195, 185])).
% 0.99/1.18 tff(197,plain,
% 0.99/1.18 ((~![A_14: $i] : iLEQ(A_14, A_14)) | iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(198,plain,
% 0.99/1.18 (iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[197, 33])).
% 0.99/1.18 tff(199,plain,
% 0.99/1.18 ((~![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(200,plain,
% 0.99/1.18 (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|)),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[199, 9])).
% 0.99/1.18 tff(201,plain,
% 0.99/1.18 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(202,plain,
% 0.99/1.18 (((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(203,plain,
% 0.99/1.18 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.18 inference(monotonicity,[status(thm)],[202])).
% 0.99/1.18 tff(204,plain,
% 0.99/1.18 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.18 inference(transitivity,[status(thm)],[203, 201])).
% 0.99/1.18 tff(205,plain,
% 0.99/1.18 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(206,plain,
% 0.99/1.18 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.18 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.99/1.18 tff(207,plain,
% 0.99/1.18 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[206, 48, 200, 198])).
% 0.99/1.18 tff(208,plain,
% 0.99/1.18 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[207, 185])).
% 0.99/1.18 tff(209,plain,
% 0.99/1.18 ((~![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))) | (~tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(210,plain,
% 0.99/1.18 (~tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.18 inference(unit_resolution,[status(thm)],[209, 20])).
% 0.99/1.18 tff(211,plain,
% 0.99/1.18 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(212,plain,
% 0.99/1.18 ((tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))))) <=> (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.18 inference(rewrite,[status(thm)],[])).
% 0.99/1.18 tff(213,plain,
% 0.99/1.18 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.18 inference(monotonicity,[status(thm)],[212])).
% 0.99/1.18 tff(214,plain,
% 0.99/1.18 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.18 inference(transitivity,[status(thm)],[213, 211])).
% 0.99/1.18 tff(215,plain,
% 0.99/1.18 ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.18 inference(quant_inst,[status(thm)],[])).
% 0.99/1.18 tff(216,plain,
% 0.99/1.18 ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.99/1.19 tff(217,plain,
% 0.99/1.19 ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[216, 67, 210])).
% 0.99/1.19 tff(218,plain,
% 0.99/1.19 ($false),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[217, 208, 196])).
% 0.99/1.19 tff(219,plain,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.19 tff(220,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))), introduced(assumption)).
% 0.99/1.19 tff(221,plain,
% 0.99/1.19 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(222,plain,
% 0.99/1.19 (((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(223,plain,
% 0.99/1.19 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.19 inference(monotonicity,[status(thm)],[222])).
% 0.99/1.19 tff(224,plain,
% 0.99/1.19 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(transitivity,[status(thm)],[223, 221])).
% 0.99/1.19 tff(225,plain,
% 0.99/1.19 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))))),
% 0.99/1.19 inference(quant_inst,[status(thm)],[])).
% 0.99/1.19 tff(226,plain,
% 0.99/1.19 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.99/1.19 tff(227,plain,
% 0.99/1.19 ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[226, 147, 187])).
% 0.99/1.19 tff(228,plain,
% 0.99/1.19 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[227, 220, 136])).
% 0.99/1.19 tff(229,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))), introduced(assumption)).
% 0.99/1.19 tff(230,plain,
% 0.99/1.19 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(231,plain,
% 0.99/1.19 (((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(232,plain,
% 0.99/1.19 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(monotonicity,[status(thm)],[231])).
% 0.99/1.19 tff(233,plain,
% 0.99/1.19 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.19 inference(transitivity,[status(thm)],[232, 230])).
% 0.99/1.19 tff(234,plain,
% 0.99/1.19 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))))),
% 0.99/1.19 inference(quant_inst,[status(thm)],[])).
% 0.99/1.19 tff(235,plain,
% 0.99/1.19 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.99/1.19 tff(236,plain,
% 0.99/1.19 (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[235, 147, 198])).
% 0.99/1.19 tff(237,plain,
% 0.99/1.19 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[236, 220, 229])).
% 0.99/1.19 tff(238,plain,
% 0.99/1.19 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(239,plain,
% 0.99/1.19 ((tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))))) <=> (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(240,plain,
% 0.99/1.19 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.19 inference(monotonicity,[status(thm)],[239])).
% 0.99/1.19 tff(241,plain,
% 0.99/1.19 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.19 inference(transitivity,[status(thm)],[240, 238])).
% 0.99/1.19 tff(242,plain,
% 0.99/1.19 ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(quant_inst,[status(thm)],[])).
% 0.99/1.19 tff(243,plain,
% 0.99/1.19 ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.99/1.19 tff(244,plain,
% 0.99/1.19 ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[243, 174, 210])).
% 0.99/1.19 tff(245,plain,
% 0.99/1.19 ($false),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[244, 237, 228])).
% 0.99/1.19 tff(246,plain,((~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.19 tff(247,plain,
% 0.99/1.19 (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[246, 219])).
% 0.99/1.19 tff(248,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))), introduced(assumption)).
% 0.99/1.19 tff(249,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.99/1.19 tff(250,plain,
% 0.99/1.19 (^[B_14: $i, A_22: $i] : refl(((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|)))))) <=> ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|)))))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(251,plain,
% 0.99/1.19 (![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|)))))) <=> ![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[250])).
% 0.99/1.19 tff(252,plain,
% 0.99/1.19 (![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|)))))) <=> ![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(253,plain,
% 0.99/1.19 (^[B_14: $i, A_22: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))) | (~iLEQ(A_22, B_14))) <=> ((~iLEQ(A_22, B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))), ((((~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))) | (~iLEQ(A_22, B_14))) | tptp_fun__E_(s(s(|'0'|)), f(B_14))) <=> (((~iLEQ(A_22, B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(|'0'|)), f(B_14))))), rewrite((((~iLEQ(A_22, B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(|'0'|)), f(B_14))) <=> ((~iLEQ(A_22, B_14)) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))), ((((~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))) | (~iLEQ(A_22, B_14))) | tptp_fun__E_(s(s(|'0'|)), f(B_14))) <=> ((~iLEQ(A_22, B_14)) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|)))))))), (((((~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))) | (~iLEQ(A_22, B_14))) | tptp_fun__E_(s(s(|'0'|)), f(B_14))) | tptp_fun__LE_(f(B_14), s(s(|'0'|)))) <=> (((~iLEQ(A_22, B_14)) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|)))))) | tptp_fun__LE_(f(B_14), s(s(|'0'|)))))), rewrite((((~iLEQ(A_22, B_14)) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|)))))) | tptp_fun__LE_(f(B_14), s(s(|'0'|)))) <=> ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))), (((((~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))) | (~iLEQ(A_22, B_14))) | tptp_fun__E_(s(s(|'0'|)), f(B_14))) | tptp_fun__LE_(f(B_14), s(s(|'0'|)))) <=> ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(254,plain,
% 0.99/1.19 (![B_14: $i, A_22: $i] : ((((~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))) | (~iLEQ(A_22, B_14))) | tptp_fun__E_(s(s(|'0'|)), f(B_14))) | tptp_fun__LE_(f(B_14), s(s(|'0'|)))) <=> ![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[253])).
% 0.99/1.19 tff(255,axiom,(![B_14: $i, A_22: $i] : ((((~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))) | (~iLEQ(A_22, B_14))) | tptp_fun__E_(s(s(|'0'|)), f(B_14))) | tptp_fun__LE_(f(B_14), s(s(|'0'|))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_51_50')).
% 0.99/1.19 tff(256,plain,
% 0.99/1.19 (![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.99/1.19 tff(257,plain,
% 0.99/1.19 (![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[256, 252])).
% 0.99/1.19 tff(258,plain,(
% 0.99/1.19 ![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))),
% 0.99/1.19 inference(skolemize,[status(sab)],[257])).
% 0.99/1.19 tff(259,plain,
% 0.99/1.19 (![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[258, 251])).
% 0.99/1.19 tff(260,plain,
% 0.99/1.19 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(261,plain,
% 0.99/1.19 (((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(262,plain,
% 0.99/1.19 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(monotonicity,[status(thm)],[261])).
% 0.99/1.19 tff(263,plain,
% 0.99/1.19 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.19 inference(transitivity,[status(thm)],[262, 260])).
% 0.99/1.19 tff(264,plain,
% 0.99/1.19 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))))),
% 0.99/1.19 inference(quant_inst,[status(thm)],[])).
% 0.99/1.19 tff(265,plain,
% 0.99/1.19 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.99/1.19 tff(266,plain,
% 0.99/1.19 (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[265, 259, 198])).
% 0.99/1.19 tff(267,plain,
% 0.99/1.19 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[266, 249, 248])).
% 0.99/1.19 tff(268,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))), introduced(assumption)).
% 0.99/1.19 tff(269,plain,
% 0.99/1.19 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(270,plain,
% 0.99/1.19 (((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))))) <=> (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(271,plain,
% 0.99/1.19 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.19 inference(monotonicity,[status(thm)],[270])).
% 0.99/1.19 tff(272,plain,
% 0.99/1.19 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.19 inference(transitivity,[status(thm)],[271, 269])).
% 0.99/1.19 tff(273,plain,
% 0.99/1.19 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))))),
% 0.99/1.19 inference(quant_inst,[status(thm)],[])).
% 0.99/1.19 tff(274,plain,
% 0.99/1.19 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.99/1.19 tff(275,plain,
% 0.99/1.19 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[274, 259, 187])).
% 0.99/1.19 tff(276,plain,
% 0.99/1.19 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[275, 249, 268])).
% 0.99/1.19 tff(277,plain,
% 0.99/1.19 (^[A_26: $i] : refl((tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26)))) <=> (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26)))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(278,plain,
% 0.99/1.19 (![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26)))) <=> ![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[277])).
% 0.99/1.19 tff(279,plain,
% 0.99/1.19 (![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26)))) <=> ![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(280,plain,
% 0.99/1.19 (^[A_26: $i] : rewrite((((~tptp_fun__E_(s(s(|'0'|)), f(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26))))) | tptp_fun__E_(f(A_26), f(g(A_26)))) <=> (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26)))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(281,plain,
% 0.99/1.19 (![A_26: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26))))) | tptp_fun__E_(f(A_26), f(g(A_26)))) <=> ![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[280])).
% 0.99/1.19 tff(282,axiom,(![A_26: $i] : (((~tptp_fun__E_(s(s(|'0'|)), f(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26))))) | tptp_fun__E_(f(A_26), f(g(A_26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_20_22')).
% 0.99/1.19 tff(283,plain,
% 0.99/1.19 (![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.99/1.19 tff(284,plain,
% 0.99/1.19 (![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[283, 279])).
% 0.99/1.19 tff(285,plain,(
% 0.99/1.19 ![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))),
% 0.99/1.19 inference(skolemize,[status(sab)],[284])).
% 0.99/1.19 tff(286,plain,
% 0.99/1.19 (![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[285, 278])).
% 0.99/1.19 tff(287,plain,
% 0.99/1.19 (((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(288,plain,
% 0.99/1.19 ((tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))))) <=> (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(289,plain,
% 0.99/1.20 (((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.20 inference(monotonicity,[status(thm)],[288])).
% 0.99/1.20 tff(290,plain,
% 0.99/1.20 (((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.20 inference(transitivity,[status(thm)],[289, 287])).
% 0.99/1.20 tff(291,plain,
% 0.99/1.20 ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.20 inference(quant_inst,[status(thm)],[])).
% 0.99/1.20 tff(292,plain,
% 0.99/1.20 ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.99/1.20 tff(293,plain,
% 0.99/1.20 ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[292, 286, 210])).
% 0.99/1.20 tff(294,plain,
% 0.99/1.20 ($false),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[293, 276, 267])).
% 0.99/1.20 tff(295,plain,((~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.20 tff(296,plain,
% 0.99/1.20 ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[295, 247])).
% 0.99/1.20 tff(297,plain,
% 0.99/1.20 (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[296, 184])).
% 0.99/1.20 tff(298,plain,
% 0.99/1.20 (^[A_19: $i, B_12: $i] : refl((tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|))))))) <=> (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|))))))))),
% 0.99/1.20 inference(bind,[status(th)],[])).
% 0.99/1.20 tff(299,plain,
% 0.99/1.20 (![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|))))))) <=> ![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))),
% 0.99/1.20 inference(quant_intro,[status(thm)],[298])).
% 0.99/1.20 tff(300,plain,
% 0.99/1.20 (![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|))))))) <=> ![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(301,plain,
% 0.99/1.20 (^[A_19: $i, B_12: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))) | (~iLEQ(A_19, B_12))) <=> ((~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))), ((((~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))) | (~iLEQ(A_19, B_12))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12))) <=> (((~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12))))), rewrite((((~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))), ((((~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))) | (~iLEQ(A_19, B_12))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|))))))))), (((((~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))) | (~iLEQ(A_19, B_12))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12))) | tptp_fun__LE_(f(B_12), s(s(s(|'0'|))))) <=> ((tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_12), s(s(s(|'0'|))))))), rewrite(((tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(B_12), s(s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))), (((((~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))) | (~iLEQ(A_19, B_12))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12))) | tptp_fun__LE_(f(B_12), s(s(s(|'0'|))))) <=> (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))))),
% 0.99/1.20 inference(bind,[status(th)],[])).
% 0.99/1.20 tff(302,plain,
% 0.99/1.20 (![A_19: $i, B_12: $i] : ((((~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))) | (~iLEQ(A_19, B_12))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12))) | tptp_fun__LE_(f(B_12), s(s(s(|'0'|))))) <=> ![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))),
% 0.99/1.20 inference(quant_intro,[status(thm)],[301])).
% 0.99/1.20 tff(303,axiom,(![A_19: $i, B_12: $i] : ((((~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))) | (~iLEQ(A_19, B_12))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12))) | tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_8_03')).
% 0.99/1.20 tff(304,plain,
% 0.99/1.20 (![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.99/1.20 tff(305,plain,
% 0.99/1.20 (![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[304, 300])).
% 0.99/1.20 tff(306,plain,(
% 0.99/1.20 ![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))),
% 0.99/1.20 inference(skolemize,[status(sab)],[305])).
% 0.99/1.20 tff(307,plain,
% 0.99/1.20 (![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[306, 299])).
% 0.99/1.20 tff(308,plain,
% 0.99/1.20 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(309,plain,
% 0.99/1.20 ((tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(310,plain,
% 0.99/1.20 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.20 inference(monotonicity,[status(thm)],[309])).
% 0.99/1.20 tff(311,plain,
% 0.99/1.20 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.20 inference(transitivity,[status(thm)],[310, 308])).
% 0.99/1.20 tff(312,plain,
% 0.99/1.20 ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))))),
% 0.99/1.20 inference(quant_inst,[status(thm)],[])).
% 0.99/1.20 tff(313,plain,
% 0.99/1.20 ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.99/1.20 tff(314,plain,
% 0.99/1.20 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[313, 307, 198])).
% 0.99/1.20 tff(315,plain,
% 0.99/1.20 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[314, 297])).
% 0.99/1.20 tff(316,plain,
% 0.99/1.20 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[315, 1])).
% 0.99/1.20 tff(317,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.99/1.20 tff(318,plain,
% 0.99/1.20 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(319,plain,
% 0.99/1.20 (((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))))) <=> ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(320,plain,
% 0.99/1.20 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))))),
% 0.99/1.20 inference(monotonicity,[status(thm)],[319])).
% 0.99/1.20 tff(321,plain,
% 0.99/1.20 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))))),
% 0.99/1.20 inference(transitivity,[status(thm)],[320, 318])).
% 0.99/1.20 tff(322,plain,
% 0.99/1.20 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))))),
% 0.99/1.20 inference(quant_inst,[status(thm)],[])).
% 0.99/1.20 tff(323,plain,
% 0.99/1.20 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.99/1.20 tff(324,plain,
% 0.99/1.20 ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(|'0'|)))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[323, 259, 104])).
% 0.99/1.20 tff(325,plain,
% 0.99/1.20 ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[324, 184])).
% 0.99/1.20 tff(326,plain,
% 0.99/1.20 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[325, 317])).
% 0.99/1.20 tff(327,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))), introduced(assumption)).
% 0.99/1.20 tff(328,assumption,(~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), introduced(assumption)).
% 0.99/1.20 tff(329,plain,
% 0.99/1.20 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(330,plain,
% 0.99/1.20 (((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(331,plain,
% 0.99/1.20 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.20 inference(monotonicity,[status(thm)],[330])).
% 0.99/1.20 tff(332,plain,
% 0.99/1.20 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.20 inference(transitivity,[status(thm)],[331, 329])).
% 0.99/1.20 tff(333,plain,
% 0.99/1.20 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))))),
% 0.99/1.20 inference(quant_inst,[status(thm)],[])).
% 0.99/1.20 tff(334,plain,
% 0.99/1.20 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.99/1.20 tff(335,plain,
% 0.99/1.20 ($false),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[334, 147, 327, 328, 93, 35])).
% 0.99/1.20 tff(336,plain,(tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.20 tff(337,plain,
% 0.99/1.20 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[336, 327])).
% 0.99/1.20 tff(338,assumption,(tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))), introduced(assumption)).
% 0.99/1.20 tff(339,assumption,(tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), introduced(assumption)).
% 0.99/1.20 tff(340,plain,
% 0.99/1.20 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(341,plain,
% 0.99/1.20 ((tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(342,plain,
% 0.99/1.20 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.20 inference(monotonicity,[status(thm)],[341])).
% 0.99/1.20 tff(343,plain,
% 0.99/1.20 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.20 inference(transitivity,[status(thm)],[342, 340])).
% 0.99/1.20 tff(344,plain,
% 0.99/1.20 ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.20 inference(quant_inst,[status(thm)],[])).
% 0.99/1.20 tff(345,plain,
% 0.99/1.20 ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.99/1.20 tff(346,plain,
% 0.99/1.20 ($false),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[345, 174, 339, 23, 338])).
% 0.99/1.20 tff(347,plain,((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.20 tff(348,plain,
% 0.99/1.20 (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[347, 337])).
% 0.99/1.20 tff(349,assumption,(tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))), introduced(assumption)).
% 0.99/1.20 tff(350,plain,
% 0.99/1.20 ((~![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))) | (~tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.20 inference(quant_inst,[status(thm)],[])).
% 0.99/1.20 tff(351,plain,
% 0.99/1.20 ($false),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[350, 20, 349])).
% 0.99/1.21 tff(352,plain,(~tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.21 tff(353,plain,
% 0.99/1.21 ((~![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), |'0'|))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(354,plain,
% 0.99/1.21 (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), |'0'|)),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[353, 9])).
% 0.99/1.21 tff(355,assumption,(~tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))), introduced(assumption)).
% 0.99/1.21 tff(356,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))), introduced(assumption)).
% 0.99/1.21 tff(357,plain,
% 0.99/1.21 ((~![A_14: $i] : iLEQ(A_14, A_14)) | iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(358,plain,
% 0.99/1.21 (iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[357, 33])).
% 0.99/1.21 tff(359,assumption,(~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))), introduced(assumption)).
% 0.99/1.21 tff(360,plain,
% 0.99/1.21 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(361,plain,
% 0.99/1.21 (((~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|)))) <=> ((~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(362,plain,
% 0.99/1.21 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|)))))),
% 0.99/1.21 inference(monotonicity,[status(thm)],[361])).
% 0.99/1.21 tff(363,plain,
% 0.99/1.21 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))))),
% 0.99/1.21 inference(transitivity,[status(thm)],[362, 360])).
% 0.99/1.21 tff(364,plain,
% 0.99/1.21 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(365,plain,
% 0.99/1.21 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|)))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.99/1.21 tff(366,plain,
% 0.99/1.21 ($false),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[365, 48, 12, 359, 356, 358])).
% 0.99/1.21 tff(367,plain,(tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.21 tff(368,plain,
% 0.99/1.21 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[367, 356])).
% 0.99/1.21 tff(369,plain,
% 0.99/1.21 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(370,plain,
% 0.99/1.21 ((tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) <=> ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(371,plain,
% 0.99/1.21 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))))),
% 0.99/1.21 inference(monotonicity,[status(thm)],[370])).
% 0.99/1.21 tff(372,plain,
% 0.99/1.21 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.21 inference(transitivity,[status(thm)],[371, 369])).
% 0.99/1.21 tff(373,plain,
% 0.99/1.21 ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(374,plain,
% 0.99/1.21 ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.99/1.21 tff(375,plain,
% 0.99/1.21 (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[374, 67, 368, 355])).
% 0.99/1.21 tff(376,plain,
% 0.99/1.21 ((~![A_23: $i] : iLEQ(A_23, g(A_23))) | iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(377,plain,
% 0.99/1.21 (iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[376, 81])).
% 0.99/1.21 tff(378,plain,
% 0.99/1.21 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(379,plain,
% 0.99/1.21 (((~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|)))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(380,plain,
% 0.99/1.21 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))))),
% 0.99/1.21 inference(monotonicity,[status(thm)],[379])).
% 0.99/1.21 tff(381,plain,
% 0.99/1.21 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))), g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.21 inference(transitivity,[status(thm)],[380, 378])).
% 0.99/1.21 tff(382,plain,
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% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(383,plain,
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% 0.99/1.21 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.99/1.21 tff(384,plain,
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% 0.99/1.21 inference(unit_resolution,[status(thm)],[383, 48, 356, 377])).
% 0.99/1.21 tff(385,plain,
% 0.99/1.21 ($false),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[384, 375, 354])).
% 0.99/1.21 tff(386,plain,(tptp_fun__E_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), f(g(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.21 tff(387,plain,
% 0.99/1.21 (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[386, 352])).
% 0.99/1.21 tff(388,plain,
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% 0.99/1.21 inference(rewrite,[status(thm)],[])).
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% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(390,plain,
% 0.99/1.21 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))))),
% 0.99/1.21 inference(monotonicity,[status(thm)],[389])).
% 0.99/1.21 tff(391,plain,
% 0.99/1.21 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.21 inference(transitivity,[status(thm)],[390, 388])).
% 0.99/1.21 tff(392,plain,
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% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(393,plain,
% 0.99/1.21 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(g(g(g(elem!0))))))))), g(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.99/1.21 tff(394,plain,
% 0.99/1.21 ($false),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[393, 147, 327, 83, 387, 348])).
% 0.99/1.21 tff(395,plain,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.21 tff(396,plain,
% 0.99/1.21 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(397,plain,
% 0.99/1.21 (((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(398,plain,
% 0.99/1.21 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.21 inference(monotonicity,[status(thm)],[397])).
% 0.99/1.21 tff(399,plain,
% 0.99/1.21 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.21 inference(transitivity,[status(thm)],[398, 396])).
% 0.99/1.21 tff(400,plain,
% 0.99/1.21 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.22 tff(401,plain,
% 0.99/1.22 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(g(elem!0)))))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~iLEQ(g(g(g(g(g(g(g(g(elem!0)))))))), g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.99/1.22 tff(402,plain,
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% 0.99/1.22 tff(403,plain,
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% 0.99/1.22 inference(unit_resolution,[status(thm)],[402, 395])).
% 0.99/1.22 tff(404,plain,
% 0.99/1.22 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[403, 317])).
% 0.99/1.22 tff(405,plain,
% 0.99/1.22 (((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(406,plain,
% 0.99/1.22 ((tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(407,plain,
% 0.99/1.22 (((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.22 inference(monotonicity,[status(thm)],[406])).
% 0.99/1.22 tff(408,plain,
% 0.99/1.22 (((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.22 inference(transitivity,[status(thm)],[407, 405])).
% 0.99/1.22 tff(409,plain,
% 0.99/1.22 ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.22 inference(quant_inst,[status(thm)],[])).
% 0.99/1.22 tff(410,plain,
% 0.99/1.22 ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(g(elem!0))))))))), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.99/1.22 tff(411,plain,
% 0.99/1.22 ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(g(elem!0)))))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[410, 286, 127])).
% 0.99/1.22 tff(412,plain,
% 0.99/1.22 ($false),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[411, 404, 326])).
% 0.99/1.22 tff(413,plain,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.22 tff(414,plain,
% 0.99/1.22 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(415,plain,
% 0.99/1.22 ((tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(416,plain,
% 0.99/1.22 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.22 inference(monotonicity,[status(thm)],[415])).
% 0.99/1.22 tff(417,plain,
% 0.99/1.22 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.22 inference(transitivity,[status(thm)],[416, 414])).
% 0.99/1.22 tff(418,plain,
% 0.99/1.22 ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))))),
% 0.99/1.22 inference(quant_inst,[status(thm)],[])).
% 0.99/1.22 tff(419,plain,
% 0.99/1.22 ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[418, 417])).
% 0.99/1.22 tff(420,plain,
% 0.99/1.22 (tptp_fun__LE_(f(g(g(g(g(g(g(g(g(elem!0))))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[419, 307, 187])).
% 0.99/1.22 tff(421,plain,
% 0.99/1.22 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[420, 1, 413])).
% 0.99/1.22 tff(422,plain,
% 0.99/1.22 (^[A_23: $i] : refl((tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23)))) <=> (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23)))))),
% 0.99/1.22 inference(bind,[status(th)],[])).
% 0.99/1.22 tff(423,plain,
% 0.99/1.22 (![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23)))) <=> ![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))),
% 0.99/1.22 inference(quant_intro,[status(thm)],[422])).
% 0.99/1.22 tff(424,plain,
% 0.99/1.22 (![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23)))) <=> ![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(425,plain,
% 0.99/1.22 (^[A_23: $i] : rewrite((((~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23))))) | tptp_fun__E_(f(A_23), f(g(A_23)))) <=> (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23)))))),
% 0.99/1.22 inference(bind,[status(th)],[])).
% 0.99/1.22 tff(426,plain,
% 0.99/1.22 (![A_23: $i] : (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23))))) | tptp_fun__E_(f(A_23), f(g(A_23)))) <=> ![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))),
% 0.99/1.22 inference(quant_intro,[status(thm)],[425])).
% 0.99/1.22 tff(427,axiom,(![A_23: $i] : (((~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23))))) | tptp_fun__E_(f(A_23), f(g(A_23))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_29_12')).
% 0.99/1.22 tff(428,plain,
% 0.99/1.22 (![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[427, 426])).
% 0.99/1.22 tff(429,plain,
% 0.99/1.22 (![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[428, 424])).
% 0.99/1.22 tff(430,plain,(
% 0.99/1.22 ![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))),
% 0.99/1.22 inference(skolemize,[status(sab)],[429])).
% 0.99/1.22 tff(431,plain,
% 0.99/1.22 (![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[430, 423])).
% 0.99/1.22 tff(432,plain,
% 0.99/1.22 (((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0))))))))))))) <=> ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(433,plain,
% 0.99/1.22 ((tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(434,plain,
% 0.99/1.22 (((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0)))))))))))))),
% 0.99/1.22 inference(monotonicity,[status(thm)],[433])).
% 0.99/1.22 tff(435,plain,
% 0.99/1.22 (((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.22 inference(transitivity,[status(thm)],[434, 432])).
% 0.99/1.22 tff(436,plain,
% 0.99/1.22 ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0))))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.22 inference(quant_inst,[status(thm)],[])).
% 0.99/1.22 tff(437,plain,
% 0.99/1.22 ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(g(elem!0)))))))), f(g(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.99/1.22 tff(438,plain,
% 0.99/1.22 ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[437, 431, 210])).
% 0.99/1.22 tff(439,plain,
% 0.99/1.22 ($false),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[438, 421, 316])).
% 0.99/1.22 tff(440,plain,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.22 tff(441,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))), introduced(assumption)).
% 0.99/1.22 tff(442,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))), introduced(assumption)).
% 0.99/1.22 tff(443,assumption,(~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))), introduced(assumption)).
% 0.99/1.22 tff(444,plain,
% 0.99/1.22 ((~![A_29: $i] : iLEQ(A_29, A_29)) | iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))),
% 0.99/1.22 inference(quant_inst,[status(thm)],[])).
% 0.99/1.22 tff(445,plain,
% 0.99/1.22 ($false),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[444, 101, 443])).
% 0.99/1.22 tff(446,plain,(iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.22 tff(447,plain,
% 0.99/1.22 ((~![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|))),
% 0.99/1.22 inference(quant_inst,[status(thm)],[])).
% 0.99/1.22 tff(448,plain,
% 0.99/1.22 (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|)),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[447, 9])).
% 0.99/1.22 tff(449,plain,
% 0.99/1.22 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(450,plain,
% 0.99/1.22 (((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)))) <=> (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(451,plain,
% 0.99/1.22 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.22 inference(monotonicity,[status(thm)],[450])).
% 0.99/1.22 tff(452,plain,
% 0.99/1.22 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.22 inference(transitivity,[status(thm)],[451, 449])).
% 0.99/1.22 tff(453,plain,
% 0.99/1.22 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))))),
% 0.99/1.22 inference(quant_inst,[status(thm)],[])).
% 0.99/1.22 tff(454,plain,
% 0.99/1.22 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0))))))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[453, 452])).
% 0.99/1.22 tff(455,plain,
% 0.99/1.22 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[454, 48, 448, 446])).
% 0.99/1.22 tff(456,plain,
% 0.99/1.22 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[455, 442])).
% 0.99/1.22 tff(457,plain,
% 0.99/1.22 ((~![A_23: $i] : iLEQ(A_23, g(A_23))) | iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))),
% 0.99/1.22 inference(quant_inst,[status(thm)],[])).
% 0.99/1.22 tff(458,plain,
% 0.99/1.22 (iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[457, 81])).
% 0.99/1.22 tff(459,plain,
% 0.99/1.22 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(460,plain,
% 0.99/1.22 (((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(461,plain,
% 0.99/1.22 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.22 inference(monotonicity,[status(thm)],[460])).
% 0.99/1.22 tff(462,plain,
% 0.99/1.22 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.22 inference(transitivity,[status(thm)],[461, 459])).
% 0.99/1.22 tff(463,plain,
% 0.99/1.22 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))))),
% 0.99/1.22 inference(quant_inst,[status(thm)],[])).
% 0.99/1.22 tff(464,plain,
% 0.99/1.22 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.99/1.22 tff(465,plain,
% 0.99/1.22 ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[464, 48, 458])).
% 0.99/1.22 tff(466,plain,
% 0.99/1.22 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[465, 442, 200])).
% 0.99/1.22 tff(467,plain,
% 0.99/1.22 ((~![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))) | (~tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.22 inference(quant_inst,[status(thm)],[])).
% 0.99/1.22 tff(468,plain,
% 0.99/1.22 (~tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[467, 20])).
% 0.99/1.22 tff(469,plain,
% 0.99/1.22 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(470,plain,
% 0.99/1.22 ((tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.23 inference(rewrite,[status(thm)],[])).
% 0.99/1.23 tff(471,plain,
% 0.99/1.23 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.23 inference(monotonicity,[status(thm)],[470])).
% 0.99/1.23 tff(472,plain,
% 0.99/1.23 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.23 inference(transitivity,[status(thm)],[471, 469])).
% 0.99/1.23 tff(473,plain,
% 0.99/1.23 ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.23 inference(quant_inst,[status(thm)],[])).
% 0.99/1.23 tff(474,plain,
% 0.99/1.23 ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.23 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.99/1.23 tff(475,plain,
% 0.99/1.23 ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[474, 67, 468])).
% 0.99/1.23 tff(476,plain,
% 0.99/1.23 ($false),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[475, 466, 456])).
% 0.99/1.23 tff(477,plain,(~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.23 tff(478,plain,
% 0.99/1.23 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)))),
% 0.99/1.23 inference(rewrite,[status(thm)],[])).
% 0.99/1.23 tff(479,plain,
% 0.99/1.23 (((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))))) <=> (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)))),
% 0.99/1.23 inference(rewrite,[status(thm)],[])).
% 0.99/1.23 tff(480,plain,
% 0.99/1.23 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))))),
% 0.99/1.23 inference(monotonicity,[status(thm)],[479])).
% 0.99/1.23 tff(481,plain,
% 0.99/1.23 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)))),
% 0.99/1.23 inference(transitivity,[status(thm)],[480, 478])).
% 0.99/1.23 tff(482,plain,
% 0.99/1.23 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))))),
% 0.99/1.23 inference(quant_inst,[status(thm)],[])).
% 0.99/1.23 tff(483,plain,
% 0.99/1.23 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))),
% 0.99/1.23 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.99/1.23 tff(484,plain,
% 0.99/1.23 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|))),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[483, 147, 446])).
% 0.99/1.23 tff(485,plain,
% 0.99/1.23 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))))),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[484, 477])).
% 0.99/1.23 tff(486,plain,
% 0.99/1.23 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[485, 441])).
% 0.99/1.23 tff(487,plain,
% 0.99/1.23 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.23 inference(rewrite,[status(thm)],[])).
% 0.99/1.23 tff(488,plain,
% 0.99/1.23 (((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.23 inference(rewrite,[status(thm)],[])).
% 0.99/1.23 tff(489,plain,
% 0.99/1.23 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.23 inference(monotonicity,[status(thm)],[488])).
% 0.99/1.23 tff(490,plain,
% 0.99/1.23 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.23 inference(transitivity,[status(thm)],[489, 487])).
% 0.99/1.23 tff(491,plain,
% 0.99/1.23 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))))),
% 0.99/1.23 inference(quant_inst,[status(thm)],[])).
% 0.99/1.23 tff(492,plain,
% 0.99/1.23 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.23 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.99/1.23 tff(493,plain,
% 0.99/1.23 ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[492, 147, 458])).
% 0.99/1.23 tff(494,plain,
% 0.99/1.23 ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[493, 219])).
% 0.99/1.23 tff(495,plain,
% 0.99/1.23 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[494, 441])).
% 0.99/1.23 tff(496,plain,
% 0.99/1.23 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.23 inference(rewrite,[status(thm)],[])).
% 0.99/1.23 tff(497,plain,
% 0.99/1.23 ((tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.23 inference(rewrite,[status(thm)],[])).
% 0.99/1.23 tff(498,plain,
% 0.99/1.23 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))))))),
% 0.99/1.23 inference(monotonicity,[status(thm)],[497])).
% 0.99/1.23 tff(499,plain,
% 0.99/1.23 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 0.99/1.23 inference(transitivity,[status(thm)],[498, 496])).
% 0.99/1.23 tff(500,plain,
% 0.99/1.23 ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.23 inference(quant_inst,[status(thm)],[])).
% 0.99/1.23 tff(501,plain,
% 0.99/1.23 ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.23 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.99/1.23 tff(502,plain,
% 0.99/1.23 ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[501, 174, 468])).
% 0.99/1.23 tff(503,plain,
% 0.99/1.23 ($false),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[502, 495, 486])).
% 0.99/1.23 tff(504,plain,(~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.23 tff(505,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))), introduced(assumption)).
% 0.99/1.23 tff(506,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))), introduced(assumption)).
% 0.99/1.23 tff(507,plain,
% 0.99/1.23 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.23 inference(rewrite,[status(thm)],[])).
% 0.99/1.23 tff(508,plain,
% 0.99/1.23 (((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.23 inference(rewrite,[status(thm)],[])).
% 0.99/1.23 tff(509,plain,
% 0.99/1.23 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))))),
% 0.99/1.23 inference(monotonicity,[status(thm)],[508])).
% 0.99/1.23 tff(510,plain,
% 0.99/1.23 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))))),
% 0.99/1.23 inference(transitivity,[status(thm)],[509, 507])).
% 0.99/1.23 tff(511,plain,
% 0.99/1.23 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))))),
% 0.99/1.23 inference(quant_inst,[status(thm)],[])).
% 0.99/1.23 tff(512,plain,
% 0.99/1.23 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))),
% 0.99/1.23 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.99/1.23 tff(513,plain,
% 0.99/1.23 ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[512, 259])).
% 1.07/1.23 tff(514,plain,
% 1.07/1.23 ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[513, 446])).
% 1.07/1.23 tff(515,plain,
% 1.07/1.23 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[514, 506, 505])).
% 1.07/1.23 tff(516,plain,
% 1.07/1.23 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(517,plain,
% 1.07/1.23 (((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(518,plain,
% 1.07/1.23 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[517])).
% 1.07/1.23 tff(519,plain,
% 1.07/1.23 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.23 inference(transitivity,[status(thm)],[518, 516])).
% 1.07/1.23 tff(520,plain,
% 1.07/1.23 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))))),
% 1.07/1.23 inference(quant_inst,[status(thm)],[])).
% 1.07/1.23 tff(521,plain,
% 1.07/1.23 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.23 inference(modus_ponens,[status(thm)],[520, 519])).
% 1.07/1.23 tff(522,plain,
% 1.07/1.23 ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[521, 259, 458])).
% 1.07/1.23 tff(523,plain,
% 1.07/1.23 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.23 inference(unit_resolution,[status(thm)],[522, 506, 248])).
% 1.07/1.23 tff(524,plain,
% 1.07/1.23 (((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))))) <=> ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(525,plain,
% 1.07/1.23 ((tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 1.07/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.23 tff(526,plain,
% 1.07/1.23 (((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))))))),
% 1.07/1.23 inference(monotonicity,[status(thm)],[525])).
% 1.07/1.23 tff(527,plain,
% 1.07/1.23 (((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 1.07/1.23 inference(transitivity,[status(thm)],[526, 524])).
% 1.07/1.23 tff(528,plain,
% 1.07/1.23 ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(529,plain,
% 1.07/1.24 ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[528, 527])).
% 1.07/1.24 tff(530,plain,
% 1.07/1.24 ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[529, 286, 468])).
% 1.07/1.24 tff(531,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[530, 523, 515])).
% 1.07/1.24 tff(532,plain,((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(|'0'|))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.24 tff(533,plain,
% 1.07/1.24 ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|)))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[532, 247])).
% 1.07/1.24 tff(534,plain,
% 1.07/1.24 (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[533, 504])).
% 1.07/1.24 tff(535,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))), introduced(assumption)).
% 1.07/1.24 tff(536,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 1.07/1.24 tff(537,plain,
% 1.07/1.24 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(538,plain,
% 1.07/1.24 ((tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(539,plain,
% 1.07/1.24 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[538])).
% 1.07/1.24 tff(540,plain,
% 1.07/1.24 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))))),
% 1.07/1.24 inference(transitivity,[status(thm)],[539, 537])).
% 1.07/1.24 tff(541,plain,
% 1.07/1.24 ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(542,plain,
% 1.07/1.24 ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[541, 540])).
% 1.07/1.24 tff(543,plain,
% 1.07/1.24 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[542, 307, 458])).
% 1.07/1.24 tff(544,plain,
% 1.07/1.24 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[543, 536, 535])).
% 1.07/1.24 tff(545,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|))))), introduced(assumption)).
% 1.07/1.24 tff(546,plain,
% 1.07/1.24 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(547,plain,
% 1.07/1.24 ((tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(548,plain,
% 1.07/1.24 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[547])).
% 1.07/1.24 tff(549,plain,
% 1.07/1.24 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))))),
% 1.07/1.24 inference(transitivity,[status(thm)],[548, 546])).
% 1.07/1.24 tff(550,plain,
% 1.07/1.24 ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(551,plain,
% 1.07/1.24 ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[550, 549])).
% 1.07/1.24 tff(552,plain,
% 1.07/1.24 (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[551, 307, 446])).
% 1.07/1.24 tff(553,plain,
% 1.07/1.24 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[552, 536, 545])).
% 1.07/1.24 tff(554,plain,
% 1.07/1.24 (((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(555,plain,
% 1.07/1.24 ((tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(556,plain,
% 1.07/1.24 (((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[555])).
% 1.07/1.24 tff(557,plain,
% 1.07/1.24 (((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.24 inference(transitivity,[status(thm)],[556, 554])).
% 1.07/1.24 tff(558,plain,
% 1.07/1.24 ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(559,plain,
% 1.07/1.24 ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[558, 557])).
% 1.07/1.24 tff(560,plain,
% 1.07/1.24 ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[559, 431, 468])).
% 1.07/1.24 tff(561,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[560, 553, 544])).
% 1.07/1.24 tff(562,plain,((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.24 tff(563,plain,
% 1.07/1.24 (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[562, 297, 534])).
% 1.07/1.24 tff(564,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 1.07/1.24 tff(565,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))), introduced(assumption)).
% 1.07/1.24 tff(566,plain,
% 1.07/1.24 (^[A_16: $i, B_10: $i] : refl(((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|)))))))) <=> ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|)))))))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(567,plain,
% 1.07/1.24 (![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|)))))))) <=> ![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[566])).
% 1.07/1.24 tff(568,plain,
% 1.07/1.24 (![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|)))))))) <=> ![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(569,plain,
% 1.07/1.24 (^[A_16: $i, B_10: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_16, B_10))) <=> ((~iLEQ(A_16, B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))), ((((~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_16, B_10))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10))) <=> (((~iLEQ(A_16, B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10))))), rewrite((((~iLEQ(A_16, B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10))) <=> ((~iLEQ(A_16, B_10)) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))), ((((~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_16, B_10))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10))) <=> ((~iLEQ(A_16, B_10)) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|)))))))))), (((((~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_16, B_10))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10))) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|)))))) <=> (((~iLEQ(A_16, B_10)) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|)))))))), rewrite((((~iLEQ(A_16, B_10)) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|)))))) <=> ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))), (((((~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_16, B_10))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10))) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|)))))) <=> ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(570,plain,
% 1.07/1.24 (![A_16: $i, B_10: $i] : ((((~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_16, B_10))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10))) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|)))))) <=> ![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))),
% 1.07/1.24 inference(quant_intro,[status(thm)],[569])).
% 1.07/1.24 tff(571,axiom,(![A_16: $i, B_10: $i] : ((((~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))) | (~iLEQ(A_16, B_10))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10))) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_0_36')).
% 1.07/1.24 tff(572,plain,
% 1.07/1.24 (![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[571, 570])).
% 1.07/1.24 tff(573,plain,
% 1.07/1.24 (![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[572, 568])).
% 1.07/1.24 tff(574,plain,(
% 1.07/1.24 ![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))),
% 1.07/1.24 inference(skolemize,[status(sab)],[573])).
% 1.07/1.24 tff(575,plain,
% 1.07/1.24 (![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[574, 567])).
% 1.07/1.24 tff(576,plain,
% 1.07/1.24 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(577,plain,
% 1.07/1.24 (((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))))) <=> (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(578,plain,
% 1.07/1.24 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[577])).
% 1.07/1.24 tff(579,plain,
% 1.07/1.24 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))))),
% 1.07/1.24 inference(transitivity,[status(thm)],[578, 576])).
% 1.07/1.24 tff(580,plain,
% 1.07/1.24 ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(581,plain,
% 1.07/1.24 ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[580, 579])).
% 1.07/1.24 tff(582,plain,
% 1.07/1.24 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[581, 575, 446])).
% 1.07/1.24 tff(583,plain,
% 1.07/1.24 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[582, 565, 564])).
% 1.07/1.24 tff(584,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 1.07/1.24 tff(585,plain,
% 1.07/1.24 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(586,plain,
% 1.07/1.24 (((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(587,plain,
% 1.07/1.24 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[586])).
% 1.07/1.25 tff(588,plain,
% 1.07/1.25 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.25 inference(transitivity,[status(thm)],[587, 585])).
% 1.07/1.25 tff(589,plain,
% 1.07/1.25 ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(590,plain,
% 1.07/1.25 ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[589, 588])).
% 1.07/1.25 tff(591,plain,
% 1.07/1.25 (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[590, 575, 458])).
% 1.07/1.25 tff(592,plain,
% 1.07/1.25 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[591, 565, 584])).
% 1.07/1.25 tff(593,plain,
% 1.07/1.25 (^[A_20: $i] : refl((tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20)))) <=> (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20)))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(594,plain,
% 1.07/1.25 (![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20)))) <=> ![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[593])).
% 1.07/1.25 tff(595,plain,
% 1.07/1.25 (![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20)))) <=> ![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(596,plain,
% 1.07/1.25 (^[A_20: $i] : rewrite((((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20))))) | tptp_fun__E_(f(A_20), f(g(A_20)))) <=> (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20)))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(597,plain,
% 1.07/1.25 (![A_20: $i] : (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20))))) | tptp_fun__E_(f(A_20), f(g(A_20)))) <=> ![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[596])).
% 1.07/1.25 tff(598,axiom,(![A_20: $i] : (((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20))))) | tptp_fun__E_(f(A_20), f(g(A_20))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_55_48')).
% 1.07/1.25 tff(599,plain,
% 1.07/1.25 (![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[598, 597])).
% 1.07/1.25 tff(600,plain,
% 1.07/1.25 (![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[599, 595])).
% 1.07/1.25 tff(601,plain,(
% 1.07/1.25 ![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))),
% 1.07/1.25 inference(skolemize,[status(sab)],[600])).
% 1.07/1.25 tff(602,plain,
% 1.07/1.25 (![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[601, 594])).
% 1.07/1.25 tff(603,plain,
% 1.07/1.25 (((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(604,plain,
% 1.07/1.25 ((tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(605,plain,
% 1.07/1.25 (((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[604])).
% 1.07/1.25 tff(606,plain,
% 1.07/1.25 (((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.25 inference(transitivity,[status(thm)],[605, 603])).
% 1.07/1.25 tff(607,plain,
% 1.07/1.25 ((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(608,plain,
% 1.07/1.25 ((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[607, 606])).
% 1.07/1.25 tff(609,plain,
% 1.07/1.25 ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[608, 602, 468])).
% 1.07/1.25 tff(610,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[609, 592, 583])).
% 1.07/1.25 tff(611,plain,((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(612,plain,
% 1.07/1.25 ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[611, 563])).
% 1.07/1.25 tff(613,plain,
% 1.07/1.25 (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[612, 440])).
% 1.07/1.25 tff(614,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))), introduced(assumption)).
% 1.07/1.25 tff(615,assumption,(~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))), introduced(assumption)).
% 1.07/1.25 tff(616,assumption,(tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), introduced(assumption)).
% 1.07/1.25 tff(617,assumption,(tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))), introduced(assumption)).
% 1.07/1.25 tff(618,plain,
% 1.07/1.25 ((~![A_23: $i] : iLEQ(A_23, g(A_23))) | iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(619,plain,
% 1.07/1.25 (iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[618, 81])).
% 1.07/1.25 tff(620,plain,
% 1.07/1.25 (^[A_7: $i, B_4: $i] : refl(((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(621,plain,
% 1.07/1.25 (![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[620])).
% 1.07/1.25 tff(622,plain,
% 1.07/1.25 (![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(623,plain,
% 1.07/1.25 (^[A_7: $i, B_4: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(A_7, B_4))) <=> ((~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(A_7, B_4))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4))) <=> (((~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4))))), rewrite((((~iLEQ(A_7, B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4))) <=> ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))), ((((~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(A_7, B_4))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4))) <=> ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|))))))))))))), (((((~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(A_7, B_4))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4))) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|))))))))) <=> (((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|))))))))))), rewrite((((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|))))))))) <=> ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))), (((((~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(A_7, B_4))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4))) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|))))))))) <=> ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(624,plain,
% 1.07/1.25 (![A_7: $i, B_4: $i] : ((((~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(A_7, B_4))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4))) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|))))))))) <=> ![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[623])).
% 1.07/1.25 tff(625,axiom,(![A_7: $i, B_4: $i] : ((((~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(A_7, B_4))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4))) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_26_19')).
% 1.07/1.25 tff(626,plain,
% 1.07/1.25 (![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[625, 624])).
% 1.07/1.25 tff(627,plain,
% 1.07/1.25 (![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[626, 622])).
% 1.07/1.25 tff(628,plain,(
% 1.07/1.25 ![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.07/1.25 inference(skolemize,[status(sab)],[627])).
% 1.07/1.25 tff(629,plain,
% 1.07/1.25 (![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[628, 621])).
% 1.07/1.25 tff(630,plain,
% 1.07/1.25 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(631,plain,
% 1.07/1.25 (((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(632,plain,
% 1.07/1.25 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[631])).
% 1.07/1.25 tff(633,plain,
% 1.07/1.25 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.07/1.25 inference(transitivity,[status(thm)],[632, 630])).
% 1.07/1.25 tff(634,plain,
% 1.07/1.25 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(635,plain,
% 1.07/1.25 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[634, 633])).
% 1.07/1.25 tff(636,plain,
% 1.07/1.25 ((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[635, 629, 619])).
% 1.07/1.25 tff(637,plain,
% 1.07/1.25 (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[636, 617, 614])).
% 1.07/1.25 tff(638,assumption,(~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))), introduced(assumption)).
% 1.07/1.25 tff(639,plain,
% 1.07/1.25 ((~![A_29: $i] : iLEQ(A_29, A_29)) | iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(640,plain,
% 1.07/1.25 ($false),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[639, 101, 638])).
% 1.07/1.25 tff(641,plain,(iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.25 tff(642,plain,
% 1.07/1.25 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(643,plain,
% 1.07/1.25 (((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.25 tff(644,plain,
% 1.07/1.25 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0))))))))),
% 1.07/1.25 inference(monotonicity,[status(thm)],[643])).
% 1.07/1.25 tff(645,plain,
% 1.07/1.25 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 1.07/1.25 inference(transitivity,[status(thm)],[644, 642])).
% 1.07/1.25 tff(646,plain,
% 1.07/1.25 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(647,plain,
% 1.07/1.25 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0))))))),
% 1.07/1.25 inference(modus_ponens,[status(thm)],[646, 645])).
% 1.07/1.25 tff(648,plain,
% 1.07/1.25 (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[647, 629, 641])).
% 1.07/1.25 tff(649,plain,
% 1.07/1.25 (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[648, 617, 615])).
% 1.07/1.25 tff(650,plain,
% 1.07/1.25 ((~![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))) | (~tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 1.07/1.25 inference(quant_inst,[status(thm)],[])).
% 1.07/1.25 tff(651,plain,
% 1.07/1.25 (~tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0)))))))),
% 1.07/1.25 inference(unit_resolution,[status(thm)],[650, 20])).
% 1.07/1.25 tff(652,plain,
% 1.07/1.25 (^[A_11: $i] : refl((tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11)))) <=> (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11)))))),
% 1.07/1.25 inference(bind,[status(th)],[])).
% 1.07/1.25 tff(653,plain,
% 1.07/1.25 (![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11)))) <=> ![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))),
% 1.07/1.25 inference(quant_intro,[status(thm)],[652])).
% 1.07/1.25 tff(654,plain,
% 1.07/1.25 (![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11)))) <=> ![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))),
% 1.07/1.25 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(655,plain,
% 1.07/1.26 (^[A_11: $i] : rewrite((((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11))))) | tptp_fun__E_(f(A_11), f(g(A_11)))) <=> (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11)))))),
% 1.07/1.26 inference(bind,[status(th)],[])).
% 1.07/1.26 tff(656,plain,
% 1.07/1.26 (![A_11: $i] : (((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11))))) | tptp_fun__E_(f(A_11), f(g(A_11)))) <=> ![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))),
% 1.07/1.26 inference(quant_intro,[status(thm)],[655])).
% 1.07/1.26 tff(657,axiom,(![A_11: $i] : (((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11))))) | tptp_fun__E_(f(A_11), f(g(A_11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_44_07')).
% 1.07/1.26 tff(658,plain,
% 1.07/1.26 (![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[657, 656])).
% 1.07/1.26 tff(659,plain,
% 1.07/1.26 (![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[658, 654])).
% 1.07/1.26 tff(660,plain,(
% 1.07/1.26 ![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))),
% 1.07/1.26 inference(skolemize,[status(sab)],[659])).
% 1.07/1.26 tff(661,plain,
% 1.07/1.26 (![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[660, 653])).
% 1.07/1.26 tff(662,plain,
% 1.07/1.26 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(663,plain,
% 1.07/1.26 ((tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(664,plain,
% 1.07/1.26 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))))))),
% 1.07/1.26 inference(monotonicity,[status(thm)],[663])).
% 1.07/1.26 tff(665,plain,
% 1.07/1.26 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.26 inference(transitivity,[status(thm)],[664, 662])).
% 1.07/1.26 tff(666,plain,
% 1.07/1.26 ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(667,plain,
% 1.07/1.26 ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[666, 665])).
% 1.07/1.26 tff(668,plain,
% 1.07/1.26 ((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))))),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[667, 661, 651])).
% 1.07/1.26 tff(669,plain,
% 1.07/1.26 ($false),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[668, 649, 637])).
% 1.07/1.26 tff(670,plain,((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.26 tff(671,plain,
% 1.07/1.26 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[670, 615, 614])).
% 1.07/1.26 tff(672,assumption,(~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))), introduced(assumption)).
% 1.07/1.26 tff(673,assumption,(~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))), introduced(assumption)).
% 1.07/1.26 tff(674,plain,
% 1.07/1.26 ((~![A_29: $i] : iLEQ(A_29, A_29)) | iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(675,plain,
% 1.07/1.26 ($false),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[674, 101, 673])).
% 1.07/1.26 tff(676,plain,(iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.26 tff(677,plain,
% 1.07/1.26 (^[A_4: $i, B_2: $i] : refl(((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.07/1.26 inference(bind,[status(th)],[])).
% 1.07/1.26 tff(678,plain,
% 1.07/1.26 (![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.07/1.26 inference(quant_intro,[status(thm)],[677])).
% 1.07/1.26 tff(679,plain,
% 1.07/1.26 (![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(680,plain,
% 1.07/1.26 (^[A_4: $i, B_2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(A_4, B_2))) <=> ((~iLEQ(A_4, B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))), ((((~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(A_4, B_2))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2))) <=> (((~iLEQ(A_4, B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2))))), rewrite((((~iLEQ(A_4, B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2))) <=> ((~iLEQ(A_4, B_2)) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))), ((((~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(A_4, B_2))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2))) <=> ((~iLEQ(A_4, B_2)) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))), (((((~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(A_4, B_2))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2))) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|)))))))))) <=> (((~iLEQ(A_4, B_2)) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|)))))))))))), rewrite((((~iLEQ(A_4, B_2)) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))), (((((~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(A_4, B_2))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2))) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))),
% 1.07/1.26 inference(bind,[status(th)],[])).
% 1.07/1.26 tff(681,plain,
% 1.07/1.26 (![A_4: $i, B_2: $i] : ((((~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(A_4, B_2))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2))) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|)))))))))) <=> ![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.07/1.26 inference(quant_intro,[status(thm)],[680])).
% 1.07/1.26 tff(682,axiom,(![A_4: $i, B_2: $i] : ((((~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(A_4, B_2))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2))) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_10_13')).
% 1.07/1.26 tff(683,plain,
% 1.07/1.26 (![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[682, 681])).
% 1.07/1.26 tff(684,plain,
% 1.07/1.26 (![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[683, 679])).
% 1.07/1.26 tff(685,plain,(
% 1.07/1.26 ![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.07/1.26 inference(skolemize,[status(sab)],[684])).
% 1.07/1.26 tff(686,plain,
% 1.07/1.26 (![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[685, 678])).
% 1.07/1.26 tff(687,plain,
% 1.07/1.26 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(688,plain,
% 1.07/1.26 (((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(689,plain,
% 1.07/1.26 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))))),
% 1.07/1.26 inference(monotonicity,[status(thm)],[688])).
% 1.07/1.26 tff(690,plain,
% 1.07/1.26 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 1.07/1.26 inference(transitivity,[status(thm)],[689, 687])).
% 1.07/1.26 tff(691,plain,
% 1.07/1.26 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(692,plain,
% 1.07/1.26 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[691, 690])).
% 1.07/1.26 tff(693,plain,
% 1.07/1.26 (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[692, 686, 676])).
% 1.07/1.26 tff(694,plain,
% 1.07/1.26 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[693, 616, 672])).
% 1.07/1.26 tff(695,assumption,(~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))), introduced(assumption)).
% 1.07/1.26 tff(696,plain,
% 1.07/1.26 ((~![A_23: $i] : iLEQ(A_23, g(A_23))) | iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(697,plain,
% 1.07/1.26 (iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[696, 81])).
% 1.07/1.26 tff(698,plain,
% 1.07/1.26 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(699,plain,
% 1.07/1.26 (((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(700,plain,
% 1.07/1.26 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))))),
% 1.07/1.26 inference(monotonicity,[status(thm)],[699])).
% 1.07/1.26 tff(701,plain,
% 1.07/1.26 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))))),
% 1.07/1.26 inference(transitivity,[status(thm)],[700, 698])).
% 1.07/1.26 tff(702,plain,
% 1.07/1.26 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(703,plain,
% 1.07/1.26 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[702, 701])).
% 1.07/1.26 tff(704,plain,
% 1.07/1.26 ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[703, 686, 697])).
% 1.07/1.26 tff(705,plain,
% 1.07/1.26 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[704, 616, 695])).
% 1.07/1.26 tff(706,plain,
% 1.07/1.26 ((~![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))) | (~tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 1.07/1.26 inference(quant_inst,[status(thm)],[])).
% 1.07/1.26 tff(707,plain,
% 1.07/1.26 (~tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))),
% 1.07/1.26 inference(unit_resolution,[status(thm)],[706, 20])).
% 1.07/1.26 tff(708,plain,
% 1.07/1.26 (^[A_8: $i] : refl((tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8)))) <=> (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8)))))),
% 1.07/1.26 inference(bind,[status(th)],[])).
% 1.07/1.26 tff(709,plain,
% 1.07/1.26 (![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8)))) <=> ![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))),
% 1.07/1.26 inference(quant_intro,[status(thm)],[708])).
% 1.07/1.26 tff(710,plain,
% 1.07/1.26 (![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8)))) <=> ![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(711,plain,
% 1.07/1.26 (^[A_8: $i] : rewrite((((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8))))) | tptp_fun__E_(f(A_8), f(g(A_8)))) <=> (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8)))))),
% 1.07/1.26 inference(bind,[status(th)],[])).
% 1.07/1.26 tff(712,plain,
% 1.07/1.26 (![A_8: $i] : (((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8))))) | tptp_fun__E_(f(A_8), f(g(A_8)))) <=> ![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))),
% 1.07/1.26 inference(quant_intro,[status(thm)],[711])).
% 1.07/1.26 tff(713,axiom,(![A_8: $i] : (((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8))))) | tptp_fun__E_(f(A_8), f(g(A_8))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_31_54')).
% 1.07/1.26 tff(714,plain,
% 1.07/1.26 (![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[713, 712])).
% 1.07/1.26 tff(715,plain,
% 1.07/1.26 (![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[714, 710])).
% 1.07/1.26 tff(716,plain,(
% 1.07/1.26 ![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))),
% 1.07/1.26 inference(skolemize,[status(sab)],[715])).
% 1.07/1.26 tff(717,plain,
% 1.07/1.26 (![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))),
% 1.07/1.26 inference(modus_ponens,[status(thm)],[716, 709])).
% 1.07/1.26 tff(718,plain,
% 1.07/1.26 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(719,plain,
% 1.07/1.26 ((tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))))),
% 1.07/1.26 inference(rewrite,[status(thm)],[])).
% 1.07/1.26 tff(720,plain,
% 1.07/1.26 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))))))),
% 1.07/1.27 inference(monotonicity,[status(thm)],[719])).
% 1.07/1.27 tff(721,plain,
% 1.07/1.27 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(transitivity,[status(thm)],[720, 718])).
% 1.07/1.27 tff(722,plain,
% 1.07/1.27 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(723,plain,
% 1.07/1.27 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[722, 721])).
% 1.07/1.27 tff(724,plain,
% 1.07/1.27 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[723, 717, 707])).
% 1.07/1.27 tff(725,plain,
% 1.07/1.27 ($false),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[724, 705, 694])).
% 1.07/1.27 tff(726,plain,((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.07/1.27 tff(727,plain,
% 1.07/1.27 (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[726, 671, 616])).
% 1.07/1.27 tff(728,plain,
% 1.07/1.27 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(729,plain,
% 1.07/1.27 (((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(730,plain,
% 1.07/1.27 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(monotonicity,[status(thm)],[729])).
% 1.07/1.27 tff(731,plain,
% 1.07/1.27 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))))),
% 1.07/1.27 inference(transitivity,[status(thm)],[730, 728])).
% 1.07/1.27 tff(732,plain,
% 1.07/1.27 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(733,plain,
% 1.07/1.27 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0))))))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[732, 731])).
% 1.07/1.27 tff(734,plain,
% 1.07/1.27 ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[733, 629, 697])).
% 1.07/1.27 tff(735,plain,
% 1.07/1.27 (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[734, 727, 615])).
% 1.07/1.27 tff(736,plain,
% 1.07/1.27 (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[668, 735])).
% 1.07/1.27 tff(737,plain,
% 1.07/1.27 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[704, 671, 616])).
% 1.07/1.27 tff(738,plain,
% 1.07/1.27 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(739,plain,
% 1.07/1.27 ((tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(740,plain,
% 1.07/1.27 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.27 inference(monotonicity,[status(thm)],[739])).
% 1.07/1.27 tff(741,plain,
% 1.07/1.27 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(transitivity,[status(thm)],[740, 738])).
% 1.07/1.27 tff(742,plain,
% 1.07/1.27 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(743,plain,
% 1.07/1.27 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0)))))))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[742, 741])).
% 1.07/1.27 tff(744,plain,
% 1.07/1.27 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[743, 717, 651])).
% 1.07/1.27 tff(745,plain,
% 1.07/1.27 (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[744, 737])).
% 1.07/1.27 tff(746,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))), introduced(assumption)).
% 1.07/1.27 tff(747,assumption,(~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))), introduced(assumption)).
% 1.07/1.27 tff(748,plain,
% 1.07/1.27 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(749,plain,
% 1.07/1.27 (((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(750,plain,
% 1.07/1.27 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.07/1.27 inference(monotonicity,[status(thm)],[749])).
% 1.07/1.27 tff(751,plain,
% 1.07/1.27 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(transitivity,[status(thm)],[750, 748])).
% 1.07/1.27 tff(752,plain,
% 1.07/1.27 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(753,plain,
% 1.07/1.27 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[752, 751])).
% 1.07/1.27 tff(754,plain,
% 1.07/1.27 ((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[753, 686, 619])).
% 1.07/1.27 tff(755,plain,
% 1.07/1.27 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[754, 747, 746])).
% 1.07/1.27 tff(756,assumption,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))), introduced(assumption)).
% 1.07/1.27 tff(757,plain,
% 1.07/1.27 ((~![A_14: $i] : iLEQ(A_14, A_14)) | iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(758,plain,
% 1.07/1.27 (iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[757, 33])).
% 1.07/1.27 tff(759,plain,
% 1.07/1.27 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(760,plain,
% 1.07/1.27 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(rewrite,[status(thm)],[])).
% 1.07/1.27 tff(761,plain,
% 1.07/1.27 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0)))))))))),
% 1.07/1.27 inference(monotonicity,[status(thm)],[760])).
% 1.07/1.27 tff(762,plain,
% 1.07/1.27 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.07/1.27 inference(transitivity,[status(thm)],[761, 759])).
% 1.07/1.27 tff(763,plain,
% 1.07/1.27 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.07/1.27 inference(quant_inst,[status(thm)],[])).
% 1.07/1.27 tff(764,plain,
% 1.07/1.27 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0)))))))),
% 1.07/1.27 inference(modus_ponens,[status(thm)],[763, 762])).
% 1.07/1.27 tff(765,plain,
% 1.07/1.27 (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[764, 686, 758])).
% 1.07/1.27 tff(766,plain,
% 1.07/1.27 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.07/1.27 inference(unit_resolution,[status(thm)],[765, 747, 746])).
% 1.07/1.27 tff(767,plain,
% 1.07/1.27 (^[A_1: $i, B_0: $i] : refl((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))),
% 1.07/1.27 inference(bind,[status(th)],[])).
% 1.07/1.27 tff(768,plain,
% 1.07/1.27 (![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.27 inference(quant_intro,[status(thm)],[767])).
% 1.12/1.27 tff(769,plain,
% 1.12/1.27 (![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.27 inference(rewrite,[status(thm)],[])).
% 1.12/1.27 tff(770,plain,
% 1.12/1.27 (^[A_1: $i, B_0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(A_1, B_0))) <=> ((~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))), ((((~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0))) <=> (((~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0))))), rewrite((((~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))), ((((~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))), (((((~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0))) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))), rewrite(((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))), (((((~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0))) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))))),
% 1.12/1.27 inference(bind,[status(th)],[])).
% 1.12/1.27 tff(771,plain,
% 1.12/1.27 (![A_1: $i, B_0: $i] : ((((~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0))) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.27 inference(quant_intro,[status(thm)],[770])).
% 1.12/1.27 tff(772,axiom,(![A_1: $i, B_0: $i] : ((((~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(A_1, B_0))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0))) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_48_04')).
% 1.12/1.28 tff(773,plain,
% 1.12/1.28 (![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.28 inference(modus_ponens,[status(thm)],[772, 771])).
% 1.12/1.28 tff(774,plain,
% 1.12/1.28 (![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.28 inference(modus_ponens,[status(thm)],[773, 769])).
% 1.12/1.28 tff(775,plain,(
% 1.12/1.28 ![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.28 inference(skolemize,[status(sab)],[774])).
% 1.12/1.28 tff(776,plain,
% 1.12/1.28 (![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.28 inference(modus_ponens,[status(thm)],[775, 768])).
% 1.12/1.28 tff(777,plain,
% 1.12/1.28 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.28 inference(rewrite,[status(thm)],[])).
% 1.12/1.28 tff(778,plain,
% 1.12/1.28 ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.28 inference(rewrite,[status(thm)],[])).
% 1.12/1.28 tff(779,plain,
% 1.12/1.28 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))),
% 1.12/1.28 inference(monotonicity,[status(thm)],[778])).
% 1.12/1.28 tff(780,plain,
% 1.12/1.28 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.28 inference(transitivity,[status(thm)],[779, 777])).
% 1.12/1.28 tff(781,plain,
% 1.12/1.28 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.28 inference(quant_inst,[status(thm)],[])).
% 1.12/1.28 tff(782,plain,
% 1.12/1.28 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.28 inference(modus_ponens,[status(thm)],[781, 780])).
% 1.12/1.28 tff(783,plain,
% 1.12/1.28 (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.28 inference(unit_resolution,[status(thm)],[782, 776, 758])).
% 1.12/1.28 tff(784,plain,
% 1.12/1.28 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.28 inference(unit_resolution,[status(thm)],[783, 766, 756])).
% 1.12/1.28 tff(785,plain,
% 1.12/1.28 (^[A_5: $i] : refl((tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5)))) <=> (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5)))))),
% 1.12/1.28 inference(bind,[status(th)],[])).
% 1.12/1.28 tff(786,plain,
% 1.12/1.28 (![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5)))) <=> ![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))),
% 1.12/1.28 inference(quant_intro,[status(thm)],[785])).
% 1.12/1.28 tff(787,plain,
% 1.12/1.28 (![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5)))) <=> ![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))),
% 1.12/1.28 inference(rewrite,[status(thm)],[])).
% 1.12/1.28 tff(788,plain,
% 1.12/1.28 (^[A_5: $i] : rewrite((((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5))))) | tptp_fun__E_(f(A_5), f(g(A_5)))) <=> (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5)))))),
% 1.12/1.28 inference(bind,[status(th)],[])).
% 1.12/1.28 tff(789,plain,
% 1.12/1.28 (![A_5: $i] : (((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5))))) | tptp_fun__E_(f(A_5), f(g(A_5)))) <=> ![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))),
% 1.12/1.28 inference(quant_intro,[status(thm)],[788])).
% 1.12/1.28 tff(790,axiom,(![A_5: $i] : (((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5))))) | tptp_fun__E_(f(A_5), f(g(A_5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_27_01')).
% 1.12/1.28 tff(791,plain,
% 1.12/1.28 (![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))),
% 1.12/1.28 inference(modus_ponens,[status(thm)],[790, 789])).
% 1.12/1.28 tff(792,plain,
% 1.12/1.28 (![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))),
% 1.12/1.28 inference(modus_ponens,[status(thm)],[791, 787])).
% 1.12/1.28 tff(793,plain,(
% 1.12/1.28 ![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))),
% 1.12/1.28 inference(skolemize,[status(sab)],[792])).
% 1.12/1.28 tff(794,plain,
% 1.12/1.28 (![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))),
% 1.12/1.28 inference(modus_ponens,[status(thm)],[793, 786])).
% 1.12/1.28 tff(795,plain,
% 1.12/1.28 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 1.12/1.28 inference(rewrite,[status(thm)],[])).
% 1.12/1.28 tff(796,plain,
% 1.12/1.28 ((tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 1.12/1.28 inference(rewrite,[status(thm)],[])).
% 1.12/1.28 tff(797,plain,
% 1.12/1.28 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.28 inference(monotonicity,[status(thm)],[796])).
% 1.12/1.28 tff(798,plain,
% 1.12/1.28 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 1.12/1.28 inference(transitivity,[status(thm)],[797, 795])).
% 1.12/1.28 tff(799,plain,
% 1.12/1.28 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))))),
% 1.12/1.28 inference(quant_inst,[status(thm)],[])).
% 1.12/1.28 tff(800,plain,
% 1.12/1.28 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.28 inference(modus_ponens,[status(thm)],[799, 798])).
% 1.12/1.28 tff(801,plain,
% 1.12/1.28 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.28 inference(unit_resolution,[status(thm)],[800, 794])).
% 1.12/1.28 tff(802,plain,
% 1.12/1.28 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))))),
% 1.12/1.28 inference(unit_resolution,[status(thm)],[801, 651])).
% 1.12/1.28 tff(803,plain,
% 1.12/1.28 (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))),
% 1.12/1.28 inference(unit_resolution,[status(thm)],[802, 784])).
% 1.12/1.28 tff(804,plain,
% 1.12/1.28 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.28 inference(rewrite,[status(thm)],[])).
% 1.12/1.28 tff(805,plain,
% 1.12/1.28 ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.28 inference(rewrite,[status(thm)],[])).
% 1.12/1.28 tff(806,plain,
% 1.12/1.28 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.28 inference(monotonicity,[status(thm)],[805])).
% 1.12/1.28 tff(807,plain,
% 1.12/1.28 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.28 inference(transitivity,[status(thm)],[806, 804])).
% 1.12/1.28 tff(808,plain,
% 1.12/1.28 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.28 inference(quant_inst,[status(thm)],[])).
% 1.12/1.28 tff(809,plain,
% 1.12/1.28 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.12/1.28 inference(modus_ponens,[status(thm)],[808, 807])).
% 1.12/1.28 tff(810,plain,
% 1.12/1.28 ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.12/1.28 inference(unit_resolution,[status(thm)],[809, 776, 697])).
% 1.12/1.28 tff(811,plain,
% 1.12/1.28 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.28 inference(unit_resolution,[status(thm)],[810, 803, 755])).
% 1.12/1.28 tff(812,plain,
% 1.12/1.28 (^[A: $i] : refl((tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.28 inference(bind,[status(th)],[])).
% 1.12/1.28 tff(813,plain,
% 1.12/1.28 (![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.28 inference(quant_intro,[status(thm)],[812])).
% 1.12/1.28 tff(814,plain,
% 1.12/1.28 (![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.28 inference(rewrite,[status(thm)],[])).
% 1.12/1.28 tff(815,axiom,(![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_49_39')).
% 1.12/1.28 tff(816,plain,
% 1.12/1.28 (![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.28 inference(modus_ponens,[status(thm)],[815, 814])).
% 1.12/1.28 tff(817,plain,(
% 1.12/1.28 ![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.28 inference(skolemize,[status(sab)],[816])).
% 1.12/1.28 tff(818,plain,
% 1.12/1.28 (![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.28 inference(modus_ponens,[status(thm)],[817, 813])).
% 1.12/1.28 tff(819,plain,
% 1.12/1.28 (((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.28 inference(rewrite,[status(thm)],[])).
% 1.12/1.28 tff(820,plain,
% 1.12/1.28 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.28 inference(quant_inst,[status(thm)],[])).
% 1.12/1.28 tff(821,plain,
% 1.12/1.28 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.28 inference(modus_ponens,[status(thm)],[820, 819])).
% 1.12/1.28 tff(822,plain,
% 1.12/1.28 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.28 inference(unit_resolution,[status(thm)],[821, 818])).
% 1.12/1.28 tff(823,plain,
% 1.12/1.28 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))),
% 1.12/1.28 inference(unit_resolution,[status(thm)],[822, 811])).
% 1.12/1.28 tff(824,plain,
% 1.12/1.28 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 1.12/1.29 inference(rewrite,[status(thm)],[])).
% 1.12/1.29 tff(825,plain,
% 1.12/1.29 ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 1.12/1.29 inference(rewrite,[status(thm)],[])).
% 1.12/1.29 tff(826,plain,
% 1.12/1.29 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0))))))))),
% 1.12/1.29 inference(monotonicity,[status(thm)],[825])).
% 1.12/1.29 tff(827,plain,
% 1.12/1.29 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 1.12/1.29 inference(transitivity,[status(thm)],[826, 824])).
% 1.12/1.29 tff(828,plain,
% 1.12/1.29 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.29 inference(quant_inst,[status(thm)],[])).
% 1.12/1.29 tff(829,plain,
% 1.12/1.29 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0))))))),
% 1.12/1.29 inference(modus_ponens,[status(thm)],[828, 827])).
% 1.12/1.29 tff(830,plain,
% 1.12/1.29 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[829, 776])).
% 1.12/1.29 tff(831,plain,
% 1.12/1.29 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[830, 641])).
% 1.12/1.29 tff(832,plain,
% 1.12/1.29 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[831, 803, 755])).
% 1.12/1.29 tff(833,plain,
% 1.12/1.29 (((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.29 inference(rewrite,[status(thm)],[])).
% 1.12/1.29 tff(834,plain,
% 1.12/1.29 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.29 inference(quant_inst,[status(thm)],[])).
% 1.12/1.29 tff(835,plain,
% 1.12/1.29 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.29 inference(modus_ponens,[status(thm)],[834, 833])).
% 1.12/1.29 tff(836,plain,
% 1.12/1.29 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[835, 818])).
% 1.12/1.29 tff(837,plain,
% 1.12/1.29 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[836, 832])).
% 1.12/1.29 tff(838,plain,
% 1.12/1.29 (^[A_2: $i] : refl((tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2)))) <=> (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2)))))),
% 1.12/1.29 inference(bind,[status(th)],[])).
% 1.12/1.29 tff(839,plain,
% 1.12/1.29 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2)))) <=> ![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))),
% 1.12/1.29 inference(quant_intro,[status(thm)],[838])).
% 1.12/1.29 tff(840,plain,
% 1.12/1.29 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2)))) <=> ![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))),
% 1.12/1.29 inference(rewrite,[status(thm)],[])).
% 1.12/1.29 tff(841,plain,
% 1.12/1.29 (^[A_2: $i] : rewrite((((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2))))) | tptp_fun__E_(f(A_2), f(g(A_2)))) <=> (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2)))))),
% 1.12/1.29 inference(bind,[status(th)],[])).
% 1.12/1.29 tff(842,plain,
% 1.12/1.29 (![A_2: $i] : (((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2))))) | tptp_fun__E_(f(A_2), f(g(A_2)))) <=> ![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))),
% 1.12/1.29 inference(quant_intro,[status(thm)],[841])).
% 1.12/1.29 tff(843,axiom,(![A_2: $i] : (((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2))))) | tptp_fun__E_(f(A_2), f(g(A_2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_42_32')).
% 1.12/1.29 tff(844,plain,
% 1.12/1.29 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))),
% 1.12/1.29 inference(modus_ponens,[status(thm)],[843, 842])).
% 1.12/1.29 tff(845,plain,
% 1.12/1.29 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))),
% 1.12/1.29 inference(modus_ponens,[status(thm)],[844, 840])).
% 1.12/1.29 tff(846,plain,(
% 1.12/1.29 ![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))),
% 1.12/1.29 inference(skolemize,[status(sab)],[845])).
% 1.12/1.29 tff(847,plain,
% 1.12/1.29 (![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))),
% 1.12/1.29 inference(modus_ponens,[status(thm)],[846, 839])).
% 1.12/1.29 tff(848,plain,
% 1.12/1.29 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 1.12/1.29 inference(rewrite,[status(thm)],[])).
% 1.12/1.29 tff(849,plain,
% 1.12/1.29 ((tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 1.12/1.29 inference(rewrite,[status(thm)],[])).
% 1.12/1.29 tff(850,plain,
% 1.12/1.29 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))))),
% 1.12/1.29 inference(monotonicity,[status(thm)],[849])).
% 1.12/1.29 tff(851,plain,
% 1.12/1.29 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))))),
% 1.12/1.29 inference(transitivity,[status(thm)],[850, 848])).
% 1.12/1.29 tff(852,plain,
% 1.12/1.29 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))))),
% 1.12/1.29 inference(quant_inst,[status(thm)],[])).
% 1.12/1.29 tff(853,plain,
% 1.12/1.29 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0))))))),
% 1.12/1.29 inference(modus_ponens,[status(thm)],[852, 851])).
% 1.12/1.29 tff(854,plain,
% 1.12/1.29 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0)))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[853, 847, 707])).
% 1.12/1.29 tff(855,plain,
% 1.12/1.29 ($false),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[854, 837, 823])).
% 1.12/1.29 tff(856,plain,(tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.29 tff(857,plain,
% 1.12/1.29 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[856, 747, 746])).
% 1.12/1.29 tff(858,plain,
% 1.12/1.29 (((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.29 inference(rewrite,[status(thm)],[])).
% 1.12/1.29 tff(859,plain,
% 1.12/1.29 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.29 inference(quant_inst,[status(thm)],[])).
% 1.12/1.29 tff(860,plain,
% 1.12/1.29 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.29 inference(modus_ponens,[status(thm)],[859, 858])).
% 1.12/1.29 tff(861,plain,
% 1.12/1.29 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[860, 818])).
% 1.12/1.29 tff(862,plain,
% 1.12/1.29 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[861, 857])).
% 1.12/1.29 tff(863,plain,
% 1.12/1.29 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.29 inference(rewrite,[status(thm)],[])).
% 1.12/1.29 tff(864,plain,
% 1.12/1.29 ((tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0)))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.29 inference(rewrite,[status(thm)],[])).
% 1.12/1.29 tff(865,plain,
% 1.12/1.29 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0))))))))))),
% 1.12/1.29 inference(monotonicity,[status(thm)],[864])).
% 1.12/1.29 tff(866,plain,
% 1.12/1.29 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.29 inference(transitivity,[status(thm)],[865, 863])).
% 1.12/1.29 tff(867,plain,
% 1.12/1.29 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))))),
% 1.12/1.29 inference(quant_inst,[status(thm)],[])).
% 1.12/1.29 tff(868,plain,
% 1.12/1.29 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0))))))))),
% 1.12/1.29 inference(modus_ponens,[status(thm)],[867, 866])).
% 1.12/1.29 tff(869,plain,
% 1.12/1.29 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0))))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[868, 847, 651])).
% 1.12/1.29 tff(870,plain,
% 1.12/1.29 (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[869, 862])).
% 1.12/1.29 tff(871,plain,
% 1.12/1.29 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[836, 870])).
% 1.12/1.29 tff(872,plain,
% 1.12/1.29 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[831, 871, 755])).
% 1.12/1.29 tff(873,plain,
% 1.12/1.29 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))))),
% 1.12/1.29 inference(rewrite,[status(thm)],[])).
% 1.12/1.29 tff(874,plain,
% 1.12/1.29 ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))))),
% 1.12/1.29 inference(rewrite,[status(thm)],[])).
% 1.12/1.29 tff(875,plain,
% 1.12/1.29 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.29 inference(monotonicity,[status(thm)],[874])).
% 1.12/1.29 tff(876,plain,
% 1.12/1.29 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))))),
% 1.12/1.29 inference(transitivity,[status(thm)],[875, 873])).
% 1.12/1.29 tff(877,plain,
% 1.12/1.29 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.29 inference(quant_inst,[status(thm)],[])).
% 1.12/1.29 tff(878,plain,
% 1.12/1.29 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.29 inference(modus_ponens,[status(thm)],[877, 876])).
% 1.12/1.29 tff(879,plain,
% 1.12/1.29 ((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[878, 776, 619])).
% 1.12/1.29 tff(880,plain,
% 1.12/1.29 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[879, 871, 766])).
% 1.12/1.29 tff(881,plain,
% 1.12/1.29 ($false),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[802, 880, 872])).
% 1.12/1.29 tff(882,plain,(tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.29 tff(883,plain,
% 1.12/1.29 (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.12/1.29 inference(unit_resolution,[status(thm)],[882, 745])).
% 1.12/1.29 tff(884,plain,
% 1.12/1.29 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.12/1.29 inference(rewrite,[status(thm)],[])).
% 1.12/1.29 tff(885,plain,
% 1.12/1.29 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.12/1.30 inference(rewrite,[status(thm)],[])).
% 1.12/1.30 tff(886,plain,
% 1.12/1.30 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0)))))))))),
% 1.12/1.30 inference(monotonicity,[status(thm)],[885])).
% 1.12/1.30 tff(887,plain,
% 1.12/1.30 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.12/1.30 inference(transitivity,[status(thm)],[886, 884])).
% 1.12/1.30 tff(888,plain,
% 1.12/1.30 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(quant_inst,[status(thm)],[])).
% 1.12/1.30 tff(889,plain,
% 1.12/1.30 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0)))))))),
% 1.12/1.30 inference(modus_ponens,[status(thm)],[888, 887])).
% 1.12/1.30 tff(890,plain,
% 1.12/1.30 ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[889, 629, 758])).
% 1.12/1.30 tff(891,plain,
% 1.12/1.30 ($false),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[890, 883, 736, 614])).
% 1.12/1.30 tff(892,plain,(tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.30 tff(893,plain,
% 1.12/1.30 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[892, 614, 615])).
% 1.12/1.30 tff(894,plain,
% 1.12/1.30 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[670, 614, 615])).
% 1.12/1.30 tff(895,assumption,(~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), introduced(assumption)).
% 1.12/1.30 tff(896,assumption,(~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), introduced(assumption)).
% 1.12/1.30 tff(897,assumption,(~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))), introduced(assumption)).
% 1.12/1.30 tff(898,plain,
% 1.12/1.30 (^[A_29: $i] : refl(iLEQ(A_29, g(A_29)) <=> iLEQ(A_29, g(A_29)))),
% 1.12/1.30 inference(bind,[status(th)],[])).
% 1.12/1.30 tff(899,plain,
% 1.12/1.30 (![A_29: $i] : iLEQ(A_29, g(A_29)) <=> ![A_29: $i] : iLEQ(A_29, g(A_29))),
% 1.12/1.30 inference(quant_intro,[status(thm)],[898])).
% 1.12/1.30 tff(900,plain,
% 1.12/1.30 (![A_29: $i] : iLEQ(A_29, g(A_29)) <=> ![A_29: $i] : iLEQ(A_29, g(A_29))),
% 1.12/1.30 inference(rewrite,[status(thm)],[])).
% 1.12/1.30 tff(901,axiom,(![A_29: $i] : iLEQ(A_29, g(A_29))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_22_56')).
% 1.12/1.30 tff(902,plain,
% 1.12/1.30 (![A_29: $i] : iLEQ(A_29, g(A_29))),
% 1.12/1.30 inference(modus_ponens,[status(thm)],[901, 900])).
% 1.12/1.30 tff(903,plain,(
% 1.12/1.30 ![A_29: $i] : iLEQ(A_29, g(A_29))),
% 1.12/1.30 inference(skolemize,[status(sab)],[902])).
% 1.12/1.30 tff(904,plain,
% 1.12/1.30 (![A_29: $i] : iLEQ(A_29, g(A_29))),
% 1.12/1.30 inference(modus_ponens,[status(thm)],[903, 899])).
% 1.12/1.30 tff(905,plain,
% 1.12/1.30 ((~![A_29: $i] : iLEQ(A_29, g(A_29))) | iLEQ(g(elem!0), g(g(elem!0)))),
% 1.12/1.30 inference(quant_inst,[status(thm)],[])).
% 1.12/1.30 tff(906,plain,
% 1.12/1.30 (iLEQ(g(elem!0), g(g(elem!0)))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[905, 904])).
% 1.12/1.30 tff(907,plain,
% 1.12/1.30 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(rewrite,[status(thm)],[])).
% 1.12/1.30 tff(908,plain,
% 1.12/1.30 ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(rewrite,[status(thm)],[])).
% 1.12/1.30 tff(909,plain,
% 1.12/1.30 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.30 inference(monotonicity,[status(thm)],[908])).
% 1.12/1.30 tff(910,plain,
% 1.12/1.30 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(transitivity,[status(thm)],[909, 907])).
% 1.12/1.30 tff(911,plain,
% 1.12/1.30 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.30 inference(quant_inst,[status(thm)],[])).
% 1.12/1.30 tff(912,plain,
% 1.12/1.30 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.12/1.30 inference(modus_ponens,[status(thm)],[911, 910])).
% 1.12/1.30 tff(913,plain,
% 1.12/1.30 ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[912, 776, 906])).
% 1.12/1.30 tff(914,plain,
% 1.12/1.30 (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[913, 897, 896])).
% 1.12/1.30 tff(915,plain,
% 1.12/1.30 (((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.30 inference(rewrite,[status(thm)],[])).
% 1.12/1.30 tff(916,plain,
% 1.12/1.30 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.30 inference(quant_inst,[status(thm)],[])).
% 1.12/1.30 tff(917,plain,
% 1.12/1.30 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(modus_ponens,[status(thm)],[916, 915])).
% 1.12/1.30 tff(918,plain,
% 1.12/1.30 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[917, 818])).
% 1.12/1.30 tff(919,plain,
% 1.12/1.30 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[918, 914])).
% 1.12/1.30 tff(920,assumption,(~iLEQ(g(g(elem!0)), g(g(elem!0)))), introduced(assumption)).
% 1.12/1.30 tff(921,plain,
% 1.12/1.30 ((~![A_29: $i] : iLEQ(A_29, A_29)) | iLEQ(g(g(elem!0)), g(g(elem!0)))),
% 1.12/1.30 inference(quant_inst,[status(thm)],[])).
% 1.12/1.30 tff(922,plain,
% 1.12/1.30 ($false),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[921, 101, 920])).
% 1.12/1.30 tff(923,plain,(iLEQ(g(g(elem!0)), g(g(elem!0)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.30 tff(924,plain,
% 1.12/1.30 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(rewrite,[status(thm)],[])).
% 1.12/1.30 tff(925,plain,
% 1.12/1.30 ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(rewrite,[status(thm)],[])).
% 1.12/1.30 tff(926,plain,
% 1.12/1.30 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.30 inference(monotonicity,[status(thm)],[925])).
% 1.12/1.30 tff(927,plain,
% 1.12/1.30 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(transitivity,[status(thm)],[926, 924])).
% 1.12/1.30 tff(928,plain,
% 1.12/1.30 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.30 inference(quant_inst,[status(thm)],[])).
% 1.12/1.30 tff(929,plain,
% 1.12/1.30 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.12/1.30 inference(modus_ponens,[status(thm)],[928, 927])).
% 1.12/1.30 tff(930,plain,
% 1.12/1.30 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[929, 776, 923])).
% 1.12/1.30 tff(931,plain,
% 1.12/1.30 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[930, 897, 896])).
% 1.12/1.30 tff(932,plain,
% 1.12/1.30 (((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.30 inference(rewrite,[status(thm)],[])).
% 1.12/1.30 tff(933,plain,
% 1.12/1.30 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.30 inference(quant_inst,[status(thm)],[])).
% 1.12/1.30 tff(934,plain,
% 1.12/1.30 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(modus_ponens,[status(thm)],[933, 932])).
% 1.12/1.30 tff(935,plain,
% 1.12/1.30 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[934, 818])).
% 1.12/1.30 tff(936,plain,
% 1.12/1.30 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[935, 931])).
% 1.12/1.30 tff(937,plain,
% 1.12/1.30 ((~![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))) | (~tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))))),
% 1.12/1.30 inference(quant_inst,[status(thm)],[])).
% 1.12/1.30 tff(938,plain,
% 1.12/1.30 (~tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[937, 20])).
% 1.12/1.30 tff(939,plain,
% 1.12/1.30 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))))),
% 1.12/1.30 inference(rewrite,[status(thm)],[])).
% 1.12/1.30 tff(940,plain,
% 1.12/1.30 ((tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))))),
% 1.12/1.30 inference(rewrite,[status(thm)],[])).
% 1.12/1.30 tff(941,plain,
% 1.12/1.30 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0)))))))),
% 1.12/1.30 inference(monotonicity,[status(thm)],[940])).
% 1.12/1.30 tff(942,plain,
% 1.12/1.30 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))))),
% 1.12/1.30 inference(transitivity,[status(thm)],[941, 939])).
% 1.12/1.30 tff(943,plain,
% 1.12/1.30 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))))),
% 1.12/1.30 inference(quant_inst,[status(thm)],[])).
% 1.12/1.30 tff(944,plain,
% 1.12/1.30 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0)))))),
% 1.12/1.30 inference(modus_ponens,[status(thm)],[943, 942])).
% 1.12/1.30 tff(945,plain,
% 1.12/1.30 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0)))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[944, 847, 938])).
% 1.12/1.30 tff(946,plain,
% 1.12/1.30 ($false),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[945, 936, 919])).
% 1.12/1.30 tff(947,plain,(tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.30 tff(948,plain,
% 1.12/1.30 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[947, 896])).
% 1.12/1.30 tff(949,plain,
% 1.12/1.30 ((~![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))) | (~tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))))),
% 1.12/1.30 inference(quant_inst,[status(thm)],[])).
% 1.12/1.30 tff(950,plain,
% 1.12/1.30 (~tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0)))))),
% 1.12/1.30 inference(unit_resolution,[status(thm)],[949, 20])).
% 1.12/1.30 tff(951,plain,
% 1.12/1.30 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))))),
% 1.12/1.30 inference(rewrite,[status(thm)],[])).
% 1.12/1.30 tff(952,plain,
% 1.12/1.30 ((tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))))),
% 1.12/1.30 inference(rewrite,[status(thm)],[])).
% 1.12/1.30 tff(953,plain,
% 1.12/1.30 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))))))),
% 1.12/1.30 inference(monotonicity,[status(thm)],[952])).
% 1.12/1.30 tff(954,plain,
% 1.12/1.30 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))))),
% 1.12/1.30 inference(transitivity,[status(thm)],[953, 951])).
% 1.12/1.30 tff(955,plain,
% 1.12/1.30 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))))),
% 1.12/1.30 inference(quant_inst,[status(thm)],[])).
% 1.12/1.30 tff(956,plain,
% 1.12/1.30 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))))),
% 1.12/1.30 inference(modus_ponens,[status(thm)],[955, 954])).
% 1.12/1.31 tff(957,plain,
% 1.12/1.31 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[956, 794, 950])).
% 1.12/1.31 tff(958,plain,
% 1.12/1.31 (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[957, 948])).
% 1.12/1.31 tff(959,plain,
% 1.12/1.31 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(960,plain,
% 1.12/1.31 ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(961,plain,
% 1.12/1.31 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))))),
% 1.12/1.31 inference(monotonicity,[status(thm)],[960])).
% 1.12/1.31 tff(962,plain,
% 1.12/1.31 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 1.12/1.31 inference(transitivity,[status(thm)],[961, 959])).
% 1.12/1.31 tff(963,plain,
% 1.12/1.31 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.31 inference(quant_inst,[status(thm)],[])).
% 1.12/1.31 tff(964,plain,
% 1.12/1.31 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))),
% 1.12/1.31 inference(modus_ponens,[status(thm)],[963, 962])).
% 1.12/1.31 tff(965,plain,
% 1.12/1.31 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[964, 776, 676])).
% 1.12/1.31 tff(966,plain,
% 1.12/1.31 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[965, 958, 895])).
% 1.12/1.31 tff(967,assumption,(tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))), introduced(assumption)).
% 1.12/1.31 tff(968,plain,
% 1.12/1.31 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[930, 967, 896])).
% 1.12/1.31 tff(969,plain,
% 1.12/1.31 ((~![A_23: $i] : iLEQ(A_23, g(A_23))) | iLEQ(g(g(elem!0)), g(g(g(elem!0))))),
% 1.12/1.31 inference(quant_inst,[status(thm)],[])).
% 1.12/1.31 tff(970,plain,
% 1.12/1.31 (iLEQ(g(g(elem!0)), g(g(g(elem!0))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[969, 81])).
% 1.12/1.31 tff(971,plain,
% 1.12/1.31 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(972,plain,
% 1.12/1.31 ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(973,plain,
% 1.12/1.31 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.31 inference(monotonicity,[status(thm)],[972])).
% 1.12/1.31 tff(974,plain,
% 1.12/1.31 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.31 inference(transitivity,[status(thm)],[973, 971])).
% 1.12/1.31 tff(975,plain,
% 1.12/1.31 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.12/1.31 inference(quant_inst,[status(thm)],[])).
% 1.12/1.31 tff(976,plain,
% 1.12/1.31 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.12/1.31 inference(modus_ponens,[status(thm)],[975, 974])).
% 1.12/1.31 tff(977,plain,
% 1.12/1.31 ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[976, 776, 970])).
% 1.12/1.31 tff(978,plain,
% 1.12/1.31 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[977, 967, 895])).
% 1.12/1.31 tff(979,plain,
% 1.12/1.31 ($false),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[957, 978, 968])).
% 1.12/1.31 tff(980,plain,((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.31 tff(981,plain,
% 1.12/1.31 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[980, 896, 895])).
% 1.12/1.31 tff(982,plain,
% 1.12/1.31 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[935, 981])).
% 1.12/1.31 tff(983,plain,
% 1.12/1.31 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))))),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(984,plain,
% 1.12/1.31 ((tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0)))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))))),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(985,plain,
% 1.12/1.31 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0))))))))),
% 1.12/1.31 inference(monotonicity,[status(thm)],[984])).
% 1.12/1.31 tff(986,plain,
% 1.12/1.31 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))))),
% 1.12/1.31 inference(transitivity,[status(thm)],[985, 983])).
% 1.12/1.31 tff(987,plain,
% 1.12/1.31 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))))),
% 1.12/1.31 inference(quant_inst,[status(thm)],[])).
% 1.12/1.31 tff(988,plain,
% 1.12/1.31 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0))))))),
% 1.12/1.31 inference(modus_ponens,[status(thm)],[987, 986])).
% 1.12/1.31 tff(989,plain,
% 1.12/1.31 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[988, 847, 950])).
% 1.12/1.31 tff(990,plain,
% 1.12/1.31 (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[989, 982])).
% 1.12/1.31 tff(991,plain,
% 1.12/1.31 ($false),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[822, 990, 966])).
% 1.12/1.31 tff(992,plain,(tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.31 tff(993,plain,
% 1.12/1.31 (tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[992, 893])).
% 1.12/1.31 tff(994,plain,
% 1.12/1.31 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(995,plain,
% 1.12/1.31 (((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(996,plain,
% 1.12/1.31 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0)))))))),
% 1.12/1.31 inference(monotonicity,[status(thm)],[995])).
% 1.12/1.31 tff(997,plain,
% 1.12/1.31 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 1.12/1.31 inference(transitivity,[status(thm)],[996, 994])).
% 1.12/1.31 tff(998,plain,
% 1.12/1.31 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.31 inference(quant_inst,[status(thm)],[])).
% 1.12/1.31 tff(999,plain,
% 1.12/1.31 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0)))))),
% 1.12/1.31 inference(modus_ponens,[status(thm)],[998, 997])).
% 1.12/1.31 tff(1000,plain,
% 1.12/1.31 ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[999, 686, 970])).
% 1.12/1.31 tff(1001,plain,
% 1.12/1.31 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[1000, 993, 672])).
% 1.12/1.31 tff(1002,plain,
% 1.12/1.31 (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[724, 1001])).
% 1.12/1.31 tff(1003,plain,
% 1.12/1.31 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(1004,plain,
% 1.12/1.31 (((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 1.12/1.31 inference(rewrite,[status(thm)],[])).
% 1.12/1.31 tff(1005,plain,
% 1.12/1.31 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0))))))))),
% 1.12/1.31 inference(monotonicity,[status(thm)],[1004])).
% 1.12/1.31 tff(1006,plain,
% 1.12/1.31 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))))),
% 1.12/1.31 inference(transitivity,[status(thm)],[1005, 1003])).
% 1.12/1.31 tff(1007,plain,
% 1.12/1.31 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.12/1.31 inference(quant_inst,[status(thm)],[])).
% 1.12/1.31 tff(1008,plain,
% 1.12/1.31 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0))))))),
% 1.12/1.31 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 1.12/1.31 tff(1009,plain,
% 1.12/1.31 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[1008, 686, 641])).
% 1.12/1.31 tff(1010,plain,
% 1.12/1.31 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[1009, 1002, 894])).
% 1.12/1.31 tff(1011,assumption,(~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), introduced(assumption)).
% 1.12/1.31 tff(1012,assumption,(~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))), introduced(assumption)).
% 1.12/1.31 tff(1013,plain,
% 1.12/1.31 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[810, 1012, 1011])).
% 1.12/1.31 tff(1014,plain,
% 1.12/1.31 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[822, 1013])).
% 1.12/1.31 tff(1015,plain,
% 1.12/1.31 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[831, 1012, 1011])).
% 1.12/1.31 tff(1016,plain,
% 1.12/1.31 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[836, 1015])).
% 1.12/1.31 tff(1017,plain,
% 1.12/1.31 ($false),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[854, 1016, 1014])).
% 1.12/1.31 tff(1018,plain,(tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.31 tff(1019,plain,
% 1.12/1.31 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))),
% 1.12/1.31 inference(unit_resolution,[status(thm)],[1018, 1010])).
% 1.12/1.31 tff(1020,plain,
% 1.12/1.31 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(1021,plain,
% 1.12/1.32 ((tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(1022,plain,
% 1.12/1.32 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(monotonicity,[status(thm)],[1021])).
% 1.12/1.32 tff(1023,plain,
% 1.12/1.32 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))))),
% 1.12/1.32 inference(transitivity,[status(thm)],[1022, 1020])).
% 1.12/1.32 tff(1024,plain,
% 1.12/1.32 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(1025,plain,
% 1.12/1.32 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 1.12/1.32 tff(1026,plain,
% 1.12/1.32 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0)))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1025, 794, 707])).
% 1.12/1.32 tff(1027,plain,
% 1.12/1.32 (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1026, 1019])).
% 1.12/1.32 tff(1028,plain,
% 1.12/1.32 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[977, 1027, 893])).
% 1.12/1.32 tff(1029,plain,
% 1.12/1.32 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[935, 1028])).
% 1.12/1.32 tff(1030,plain,
% 1.12/1.32 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[965, 1027, 893])).
% 1.12/1.32 tff(1031,plain,
% 1.12/1.32 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[822, 1030])).
% 1.12/1.32 tff(1032,plain,
% 1.12/1.32 ($false),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[989, 1031, 1029])).
% 1.12/1.32 tff(1033,plain,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.32 tff(1034,plain,
% 1.12/1.32 (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1033, 614, 615])).
% 1.12/1.32 tff(1035,plain,
% 1.12/1.32 (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[734, 1034, 615])).
% 1.12/1.32 tff(1036,plain,
% 1.12/1.32 (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[668, 1035])).
% 1.12/1.32 tff(1037,plain,
% 1.12/1.32 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[890, 1036, 614])).
% 1.12/1.32 tff(1038,plain,
% 1.12/1.32 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[882, 1037])).
% 1.12/1.32 tff(1039,plain,
% 1.12/1.32 (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[744, 1038])).
% 1.12/1.32 tff(1040,plain,
% 1.12/1.32 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1009, 1039, 894])).
% 1.12/1.32 tff(1041,plain,
% 1.12/1.32 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1018, 1040])).
% 1.12/1.32 tff(1042,plain,
% 1.12/1.32 (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1026, 1041])).
% 1.12/1.32 tff(1043,plain,
% 1.12/1.32 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[977, 1042, 893])).
% 1.12/1.32 tff(1044,plain,
% 1.12/1.32 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[935, 1043])).
% 1.12/1.32 tff(1045,plain,
% 1.12/1.32 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[965, 1042, 893])).
% 1.12/1.32 tff(1046,plain,
% 1.12/1.32 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[822, 1045])).
% 1.12/1.32 tff(1047,plain,
% 1.12/1.32 ($false),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[989, 1046, 1044])).
% 1.12/1.32 tff(1048,plain,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.32 tff(1049,plain,
% 1.12/1.32 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1048, 614])).
% 1.12/1.32 tff(1050,assumption,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))), introduced(assumption)).
% 1.12/1.32 tff(1051,plain,
% 1.12/1.32 ((~![A_23: $i] : iLEQ(A_23, g(A_23))) | iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(1052,plain,
% 1.12/1.32 (iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1051, 81])).
% 1.12/1.32 tff(1053,plain,
% 1.12/1.32 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(1054,plain,
% 1.12/1.32 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(1055,plain,
% 1.12/1.32 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))))),
% 1.12/1.32 inference(monotonicity,[status(thm)],[1054])).
% 1.12/1.32 tff(1056,plain,
% 1.12/1.32 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(transitivity,[status(thm)],[1055, 1053])).
% 1.12/1.32 tff(1057,plain,
% 1.12/1.32 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(1058,plain,
% 1.12/1.32 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[1057, 1056])).
% 1.12/1.32 tff(1059,plain,
% 1.12/1.32 (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1058, 259, 1052])).
% 1.12/1.32 tff(1060,plain,
% 1.12/1.32 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1059, 1050, 504])).
% 1.12/1.32 tff(1061,assumption,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))), introduced(assumption)).
% 1.12/1.32 tff(1062,plain,
% 1.12/1.32 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(1063,plain,
% 1.12/1.32 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))))) <=> (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(1064,plain,
% 1.12/1.32 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))))),
% 1.12/1.32 inference(monotonicity,[status(thm)],[1063])).
% 1.12/1.32 tff(1065,plain,
% 1.12/1.32 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(transitivity,[status(thm)],[1064, 1062])).
% 1.12/1.32 tff(1066,plain,
% 1.12/1.32 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(1067,plain,
% 1.12/1.32 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 1.12/1.32 tff(1068,plain,
% 1.12/1.32 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1067, 147, 1052])).
% 1.12/1.32 tff(1069,plain,
% 1.12/1.32 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1068, 477])).
% 1.12/1.32 tff(1070,plain,
% 1.12/1.32 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1069, 1061])).
% 1.12/1.32 tff(1071,assumption,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))), introduced(assumption)).
% 1.12/1.32 tff(1072,plain,
% 1.12/1.32 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(1073,plain,
% 1.12/1.32 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)))) <=> (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(1074,plain,
% 1.12/1.32 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))))),
% 1.12/1.32 inference(monotonicity,[status(thm)],[1073])).
% 1.12/1.32 tff(1075,plain,
% 1.12/1.32 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(transitivity,[status(thm)],[1074, 1072])).
% 1.12/1.32 tff(1076,plain,
% 1.12/1.32 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(1077,plain,
% 1.12/1.32 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[1076, 1075])).
% 1.12/1.32 tff(1078,plain,
% 1.12/1.32 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), |'0'|) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1077, 48, 1052])).
% 1.12/1.32 tff(1079,plain,
% 1.12/1.32 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1078, 448])).
% 1.12/1.32 tff(1080,plain,
% 1.12/1.32 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1079, 1071])).
% 1.12/1.32 tff(1081,plain,
% 1.12/1.32 ((~![A_30: $i] : (~tptp_fun__LE_(f(g(A_30)), |'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(1082,plain,
% 1.12/1.32 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|)),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1081, 9])).
% 1.12/1.32 tff(1083,plain,
% 1.12/1.32 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(1084,plain,
% 1.12/1.32 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)))) <=> (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(1085,plain,
% 1.12/1.32 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)))))),
% 1.12/1.32 inference(monotonicity,[status(thm)],[1084])).
% 1.12/1.32 tff(1086,plain,
% 1.12/1.32 (((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))) <=> ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))),
% 1.12/1.32 inference(transitivity,[status(thm)],[1085, 1083])).
% 1.12/1.32 tff(1087,plain,
% 1.12/1.32 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(1088,plain,
% 1.12/1.32 ((~![B_18: $i, A_28: $i] : ((~iLEQ(A_28, B_18)) | tptp_fun__LE_(f(B_18), |'0'|) | tptp_fun__E_(|'0'|, f(B_18)) | (~tptp_fun__LE_(f(A_28), s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), |'0'|) | tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)))),
% 1.12/1.32 inference(modus_ponens,[status(thm)],[1087, 1086])).
% 1.12/1.32 tff(1089,plain,
% 1.12/1.32 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1088, 48, 1082, 758])).
% 1.12/1.32 tff(1090,plain,
% 1.12/1.32 (tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1089, 1071])).
% 1.12/1.32 tff(1091,plain,
% 1.12/1.32 ((~![A_14: $i] : (~tptp_fun__E_(f(A_14), f(g(A_14))))) | (~tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(quant_inst,[status(thm)],[])).
% 1.12/1.32 tff(1092,plain,
% 1.12/1.32 (~tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.32 inference(unit_resolution,[status(thm)],[1091, 20])).
% 1.12/1.32 tff(1093,plain,
% 1.12/1.32 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(1094,plain,
% 1.12/1.32 ((tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0))))))))) <=> ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.32 inference(rewrite,[status(thm)],[])).
% 1.12/1.32 tff(1095,plain,
% 1.12/1.32 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.12/1.32 inference(monotonicity,[status(thm)],[1094])).
% 1.12/1.32 tff(1096,plain,
% 1.12/1.32 (((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[1095, 1093])).
% 1.12/1.33 tff(1097,plain,
% 1.12/1.33 ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(1098,plain,
% 1.12/1.33 ((~![A_30: $i] : (tptp_fun__E_(f(A_30), f(g(A_30))) | (~tptp_fun__E_(|'0'|, f(g(A_30)))) | (~tptp_fun__E_(|'0'|, f(A_30))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 1.12/1.33 tff(1099,plain,
% 1.12/1.33 ((~tptp_fun__E_(|'0'|, f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(|'0'|, f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1098, 67, 1092])).
% 1.12/1.33 tff(1100,plain,
% 1.12/1.33 ($false),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1099, 1090, 1080])).
% 1.12/1.33 tff(1101,plain,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.33 tff(1102,plain,
% 1.12/1.33 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1103,plain,
% 1.12/1.33 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))))) <=> (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1104,plain,
% 1.12/1.33 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[1103])).
% 1.12/1.33 tff(1105,plain,
% 1.12/1.33 (((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))) <=> ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[1104, 1102])).
% 1.12/1.33 tff(1106,plain,
% 1.12/1.33 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(1107,plain,
% 1.12/1.33 ((~![B_16: $i, A_25: $i] : ((~iLEQ(A_25, B_16)) | tptp_fun__LE_(f(B_16), s(|'0'|)) | tptp_fun__E_(s(|'0'|), f(B_16)) | (~tptp_fun__LE_(f(A_25), s(s(|'0'|)))))) | tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0)))))))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[1106, 1105])).
% 1.12/1.33 tff(1108,plain,
% 1.12/1.33 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(|'0'|)) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1107, 147, 758])).
% 1.12/1.33 tff(1109,plain,
% 1.12/1.33 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1108, 1101])).
% 1.12/1.33 tff(1110,plain,
% 1.12/1.33 (tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1109, 1061])).
% 1.12/1.33 tff(1111,plain,
% 1.12/1.33 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1112,plain,
% 1.12/1.33 ((tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))))) <=> ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1113,plain,
% 1.12/1.33 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[1112])).
% 1.12/1.33 tff(1114,plain,
% 1.12/1.33 (((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[1113, 1111])).
% 1.12/1.33 tff(1115,plain,
% 1.12/1.33 ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(1116,plain,
% 1.12/1.33 ((~![A_29: $i] : (tptp_fun__E_(f(A_29), f(g(A_29))) | (~tptp_fun__E_(s(|'0'|), f(g(A_29)))) | (~tptp_fun__E_(s(|'0'|), f(A_29))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 1.12/1.33 tff(1117,plain,
% 1.12/1.33 ((~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(|'0'|), f(g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1116, 174, 1092])).
% 1.12/1.33 tff(1118,plain,
% 1.12/1.33 ($false),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1117, 1110, 1070])).
% 1.12/1.33 tff(1119,plain,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|)))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.33 tff(1120,plain,
% 1.12/1.33 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1121,plain,
% 1.12/1.33 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))))) <=> (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1122,plain,
% 1.12/1.33 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[1121])).
% 1.12/1.33 tff(1123,plain,
% 1.12/1.33 (((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))) <=> ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[1122, 1120])).
% 1.12/1.33 tff(1124,plain,
% 1.12/1.33 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(1125,plain,
% 1.12/1.33 ((~![B_14: $i, A_22: $i] : ((~iLEQ(A_22, B_14)) | tptp_fun__LE_(f(B_14), s(s(|'0'|))) | tptp_fun__E_(s(s(|'0'|)), f(B_14)) | (~tptp_fun__LE_(f(A_22), s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[1124, 1123])).
% 1.12/1.33 tff(1126,plain,
% 1.12/1.33 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(|'0'|))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1125, 259, 758])).
% 1.12/1.33 tff(1127,plain,
% 1.12/1.33 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1126, 1050, 1119])).
% 1.12/1.33 tff(1128,plain,
% 1.12/1.33 (((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1129,plain,
% 1.12/1.33 ((tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))))) <=> ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1130,plain,
% 1.12/1.33 (((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[1129])).
% 1.12/1.33 tff(1131,plain,
% 1.12/1.33 (((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[1130, 1128])).
% 1.12/1.33 tff(1132,plain,
% 1.12/1.33 ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(1133,plain,
% 1.12/1.33 ((~![A_26: $i] : (tptp_fun__E_(f(A_26), f(g(A_26))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(A_26)))) | (~tptp_fun__E_(s(s(|'0'|)), f(A_26))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[1132, 1131])).
% 1.12/1.33 tff(1134,plain,
% 1.12/1.33 ((~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1133, 286, 1092])).
% 1.12/1.33 tff(1135,plain,
% 1.12/1.33 ($false),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1134, 1127, 1060])).
% 1.12/1.33 tff(1136,plain,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.33 tff(1137,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))), introduced(assumption)).
% 1.12/1.33 tff(1138,assumption,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 1.12/1.33 tff(1139,plain,
% 1.12/1.33 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1140,plain,
% 1.12/1.33 ((tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))))) <=> (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1141,plain,
% 1.12/1.33 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[1140])).
% 1.12/1.33 tff(1142,plain,
% 1.12/1.33 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[1141, 1139])).
% 1.12/1.33 tff(1143,plain,
% 1.12/1.33 ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(1144,plain,
% 1.12/1.33 ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0)))))))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[1143, 1142])).
% 1.12/1.33 tff(1145,plain,
% 1.12/1.33 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1144, 307, 758])).
% 1.12/1.33 tff(1146,plain,
% 1.12/1.33 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1145, 1138, 1137])).
% 1.12/1.33 tff(1147,plain,
% 1.12/1.33 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1148,plain,
% 1.12/1.33 ((tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1149,plain,
% 1.12/1.33 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))))),
% 1.12/1.33 inference(monotonicity,[status(thm)],[1148])).
% 1.12/1.33 tff(1150,plain,
% 1.12/1.33 (((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))))) <=> ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(transitivity,[status(thm)],[1149, 1147])).
% 1.12/1.33 tff(1151,plain,
% 1.12/1.33 ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))))),
% 1.12/1.33 inference(quant_inst,[status(thm)],[])).
% 1.12/1.33 tff(1152,plain,
% 1.12/1.33 ((~![A_19: $i, B_12: $i] : (tptp_fun__LE_(f(B_12), s(s(s(|'0'|)))) | tptp_fun__E_(s(s(s(|'0'|))), f(B_12)) | (~iLEQ(A_19, B_12)) | (~tptp_fun__LE_(f(A_19), s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(modus_ponens,[status(thm)],[1151, 1150])).
% 1.12/1.33 tff(1153,plain,
% 1.12/1.33 (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1152, 307, 1052])).
% 1.12/1.33 tff(1154,plain,
% 1.12/1.33 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.33 inference(unit_resolution,[status(thm)],[1153, 1138, 545])).
% 1.12/1.33 tff(1155,plain,
% 1.12/1.33 (((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.33 inference(rewrite,[status(thm)],[])).
% 1.12/1.33 tff(1156,plain,
% 1.12/1.33 ((tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))))) <=> ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.34 inference(rewrite,[status(thm)],[])).
% 1.12/1.34 tff(1157,plain,
% 1.12/1.34 (((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.12/1.34 inference(monotonicity,[status(thm)],[1156])).
% 1.12/1.34 tff(1158,plain,
% 1.12/1.34 (((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.34 inference(transitivity,[status(thm)],[1157, 1155])).
% 1.12/1.34 tff(1159,plain,
% 1.12/1.34 ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))))),
% 1.12/1.34 inference(quant_inst,[status(thm)],[])).
% 1.12/1.34 tff(1160,plain,
% 1.12/1.34 ((~![A_23: $i] : (tptp_fun__E_(f(A_23), f(g(A_23))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(A_23)))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(A_23))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.12/1.34 inference(modus_ponens,[status(thm)],[1159, 1158])).
% 1.12/1.34 tff(1161,plain,
% 1.12/1.34 ((~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(elem!0))))))))),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[1160, 431, 1092])).
% 1.12/1.34 tff(1162,plain,
% 1.12/1.34 ($false),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[1161, 1154, 1146])).
% 1.12/1.34 tff(1163,plain,((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(|'0'|)))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))), inference(lemma,lemma(discharge,[]))).
% 1.12/1.34 tff(1164,plain,
% 1.12/1.34 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))),
% 1.12/1.34 inference(unit_resolution,[status(thm)],[1163, 1136, 534])).
% 1.12/1.34 tff(1165,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))), introduced(assumption)).
% 1.12/1.34 tff(1166,assumption,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))), introduced(assumption)).
% 1.12/1.34 tff(1167,plain,
% 1.12/1.34 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(1168,plain,
% 1.18/1.34 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(1169,plain,
% 1.18/1.34 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0)))))))))),
% 1.18/1.34 inference(monotonicity,[status(thm)],[1168])).
% 1.18/1.34 tff(1170,plain,
% 1.18/1.34 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.18/1.34 inference(transitivity,[status(thm)],[1169, 1167])).
% 1.18/1.34 tff(1171,plain,
% 1.18/1.34 ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))))),
% 1.18/1.34 inference(quant_inst,[status(thm)],[])).
% 1.18/1.34 tff(1172,plain,
% 1.18/1.34 ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0)))))))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 1.18/1.34 tff(1173,plain,
% 1.18/1.34 ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1172, 575, 758])).
% 1.18/1.34 tff(1174,plain,
% 1.18/1.34 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1173, 1166, 1165])).
% 1.18/1.34 tff(1175,plain,
% 1.18/1.34 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(1176,plain,
% 1.18/1.34 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(1177,plain,
% 1.18/1.34 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))))),
% 1.18/1.34 inference(monotonicity,[status(thm)],[1176])).
% 1.18/1.34 tff(1178,plain,
% 1.18/1.34 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.34 inference(transitivity,[status(thm)],[1177, 1175])).
% 1.18/1.34 tff(1179,plain,
% 1.18/1.34 ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))))),
% 1.18/1.34 inference(quant_inst,[status(thm)],[])).
% 1.18/1.34 tff(1180,plain,
% 1.18/1.34 ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[1179, 1178])).
% 1.18/1.34 tff(1181,plain,
% 1.18/1.34 ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1180, 575, 1052])).
% 1.18/1.34 tff(1182,plain,
% 1.18/1.34 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1181, 1166, 564])).
% 1.18/1.34 tff(1183,plain,
% 1.18/1.34 (((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(1184,plain,
% 1.18/1.34 ((tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0))))))))) <=> ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(1185,plain,
% 1.18/1.34 (((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.18/1.34 inference(monotonicity,[status(thm)],[1184])).
% 1.18/1.34 tff(1186,plain,
% 1.18/1.34 (((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.34 inference(transitivity,[status(thm)],[1185, 1183])).
% 1.18/1.34 tff(1187,plain,
% 1.18/1.34 ((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.34 inference(quant_inst,[status(thm)],[])).
% 1.18/1.34 tff(1188,plain,
% 1.18/1.34 ((~![A_20: $i] : (tptp_fun__E_(f(A_20), f(g(A_20))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(A_20)))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(A_20))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 1.18/1.34 tff(1189,plain,
% 1.18/1.34 ((~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1188, 602, 1092])).
% 1.18/1.34 tff(1190,plain,
% 1.18/1.34 ($false),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1189, 1182, 1174])).
% 1.18/1.34 tff(1191,plain,((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.34 tff(1192,plain,
% 1.18/1.34 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))),
% 1.18/1.34 inference(unit_resolution,[status(thm)],[1191, 563, 1164])).
% 1.18/1.34 tff(1193,assumption,(tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))), introduced(assumption)).
% 1.18/1.34 tff(1194,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))), introduced(assumption)).
% 1.18/1.34 tff(1195,assumption,(~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))), introduced(assumption)).
% 1.18/1.34 tff(1196,plain,
% 1.18/1.34 (^[B_8: $i, A_13: $i] : refl((tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|))))))))) <=> (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.34 inference(bind,[status(th)],[])).
% 1.18/1.34 tff(1197,plain,
% 1.18/1.34 (![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|))))))))) <=> ![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.34 inference(quant_intro,[status(thm)],[1196])).
% 1.18/1.34 tff(1198,plain,
% 1.18/1.34 (![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|))))))))) <=> ![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(1199,plain,
% 1.18/1.34 (^[B_8: $i, A_13: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(A_13, B_8))) <=> ((~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))), ((((~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(A_13, B_8))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8))) <=> (((~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8))))), rewrite((((~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8))) <=> (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))), ((((~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(A_13, B_8))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8))) <=> (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|))))))))))), (((((~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(A_13, B_8))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8))) | tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|))))))) <=> ((tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|))))))))), rewrite(((tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|))))))) <=> (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))), (((((~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(A_13, B_8))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8))) | tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|))))))) <=> (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))))),
% 1.18/1.34 inference(bind,[status(th)],[])).
% 1.18/1.34 tff(1200,plain,
% 1.18/1.34 (![B_8: $i, A_13: $i] : ((((~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(A_13, B_8))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8))) | tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|))))))) <=> ![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.34 inference(quant_intro,[status(thm)],[1199])).
% 1.18/1.34 tff(1201,axiom,(![B_8: $i, A_13: $i] : ((((~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(A_13, B_8))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8))) | tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_5_11')).
% 1.18/1.34 tff(1202,plain,
% 1.18/1.34 (![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[1201, 1200])).
% 1.18/1.34 tff(1203,plain,
% 1.18/1.34 (![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[1202, 1198])).
% 1.18/1.34 tff(1204,plain,(
% 1.18/1.34 ![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.34 inference(skolemize,[status(sab)],[1203])).
% 1.18/1.34 tff(1205,plain,
% 1.18/1.34 (![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.34 inference(modus_ponens,[status(thm)],[1204, 1197])).
% 1.18/1.34 tff(1206,plain,
% 1.18/1.34 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(1207,plain,
% 1.18/1.34 ((tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))))) <=> ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))))),
% 1.18/1.34 inference(rewrite,[status(thm)],[])).
% 1.18/1.34 tff(1208,plain,
% 1.18/1.34 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[1207])).
% 1.18/1.35 tff(1209,plain,
% 1.18/1.35 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))))),
% 1.18/1.35 inference(transitivity,[status(thm)],[1208, 1206])).
% 1.18/1.35 tff(1210,plain,
% 1.18/1.35 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(1211,plain,
% 1.18/1.35 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[1210, 1209])).
% 1.18/1.35 tff(1212,plain,
% 1.18/1.35 ((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1211, 1205, 619])).
% 1.18/1.35 tff(1213,plain,
% 1.18/1.35 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|)))))))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1212, 1195, 1194])).
% 1.18/1.35 tff(1214,plain,
% 1.18/1.35 (^[B_6: $i, A_10: $i] : refl(((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.18/1.35 inference(bind,[status(th)],[])).
% 1.18/1.35 tff(1215,plain,
% 1.18/1.35 (![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.35 inference(quant_intro,[status(thm)],[1214])).
% 1.18/1.35 tff(1216,plain,
% 1.18/1.35 (![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(1217,plain,
% 1.18/1.35 (^[B_6: $i, A_10: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(A_10, B_6))) <=> ((~iLEQ(A_10, B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))), ((((~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(A_10, B_6))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6))) <=> (((~iLEQ(A_10, B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6))))), rewrite((((~iLEQ(A_10, B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6))) <=> ((~iLEQ(A_10, B_6)) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))), ((((~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(A_10, B_6))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6))) <=> ((~iLEQ(A_10, B_6)) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|)))))))))))), (((((~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(A_10, B_6))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6))) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|)))))))) <=> (((~iLEQ(A_10, B_6)) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|)))))))))), rewrite((((~iLEQ(A_10, B_6)) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|)))))))) <=> ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))), (((((~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(A_10, B_6))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6))) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|)))))))) <=> ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.18/1.35 inference(bind,[status(th)],[])).
% 1.18/1.35 tff(1218,plain,
% 1.18/1.35 (![B_6: $i, A_10: $i] : ((((~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(A_10, B_6))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6))) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|)))))))) <=> ![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.35 inference(quant_intro,[status(thm)],[1217])).
% 1.18/1.35 tff(1219,axiom,(![B_6: $i, A_10: $i] : ((((~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(A_10, B_6))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6))) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_54_45')).
% 1.18/1.35 tff(1220,plain,
% 1.18/1.35 (![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 1.18/1.35 tff(1221,plain,
% 1.18/1.35 (![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[1220, 1216])).
% 1.18/1.35 tff(1222,plain,(
% 1.18/1.35 ![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.35 inference(skolemize,[status(sab)],[1221])).
% 1.18/1.35 tff(1223,plain,
% 1.18/1.35 (![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[1222, 1215])).
% 1.18/1.35 tff(1224,plain,
% 1.18/1.35 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(1225,plain,
% 1.18/1.35 (((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))))) <=> (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(1226,plain,
% 1.18/1.35 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[1225])).
% 1.18/1.35 tff(1227,plain,
% 1.18/1.35 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.35 inference(transitivity,[status(thm)],[1226, 1224])).
% 1.18/1.35 tff(1228,plain,
% 1.18/1.35 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(1229,plain,
% 1.18/1.35 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 1.18/1.35 tff(1230,plain,
% 1.18/1.35 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1229, 1223, 641])).
% 1.18/1.35 tff(1231,plain,
% 1.18/1.35 (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1230, 1213, 1193])).
% 1.18/1.35 tff(1232,plain,
% 1.18/1.35 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(1233,plain,
% 1.18/1.35 ((tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))))) <=> (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(1234,plain,
% 1.18/1.35 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0)))))))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[1233])).
% 1.18/1.35 tff(1235,plain,
% 1.18/1.35 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))))),
% 1.18/1.35 inference(transitivity,[status(thm)],[1234, 1232])).
% 1.18/1.35 tff(1236,plain,
% 1.18/1.35 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(1237,plain,
% 1.18/1.35 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0)))))))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 1.18/1.35 tff(1238,plain,
% 1.18/1.35 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1237, 1205, 758])).
% 1.18/1.35 tff(1239,plain,
% 1.18/1.35 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1238, 1195, 1194])).
% 1.18/1.35 tff(1240,plain,
% 1.18/1.35 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(1241,plain,
% 1.18/1.35 (((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(1242,plain,
% 1.18/1.35 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.35 inference(monotonicity,[status(thm)],[1241])).
% 1.18/1.35 tff(1243,plain,
% 1.18/1.35 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))))),
% 1.18/1.35 inference(transitivity,[status(thm)],[1242, 1240])).
% 1.18/1.35 tff(1244,plain,
% 1.18/1.35 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.35 inference(quant_inst,[status(thm)],[])).
% 1.18/1.35 tff(1245,plain,
% 1.18/1.35 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(elem!0)))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 1.18/1.35 tff(1246,plain,
% 1.18/1.35 ((~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1245, 1223, 619])).
% 1.18/1.35 tff(1247,plain,
% 1.18/1.35 (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))),
% 1.18/1.35 inference(unit_resolution,[status(thm)],[1246, 1239, 1193])).
% 1.18/1.35 tff(1248,plain,
% 1.18/1.35 (^[A_14: $i] : refl((tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14)))) <=> (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14)))))),
% 1.18/1.35 inference(bind,[status(th)],[])).
% 1.18/1.35 tff(1249,plain,
% 1.18/1.35 (![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14)))) <=> ![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))),
% 1.18/1.35 inference(quant_intro,[status(thm)],[1248])).
% 1.18/1.35 tff(1250,plain,
% 1.18/1.35 (![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14)))) <=> ![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(1251,plain,
% 1.18/1.35 (^[A_14: $i] : rewrite((((~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14))))) | tptp_fun__E_(f(A_14), f(g(A_14)))) <=> (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14)))))),
% 1.18/1.35 inference(bind,[status(th)],[])).
% 1.18/1.35 tff(1252,plain,
% 1.18/1.35 (![A_14: $i] : (((~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14))))) | tptp_fun__E_(f(A_14), f(g(A_14)))) <=> ![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))),
% 1.18/1.35 inference(quant_intro,[status(thm)],[1251])).
% 1.18/1.35 tff(1253,axiom,(![A_14: $i] : (((~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14))))) | tptp_fun__E_(f(A_14), f(g(A_14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_11_16')).
% 1.18/1.35 tff(1254,plain,
% 1.18/1.35 (![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[1253, 1252])).
% 1.18/1.35 tff(1255,plain,
% 1.18/1.35 (![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[1254, 1250])).
% 1.18/1.35 tff(1256,plain,(
% 1.18/1.35 ![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))),
% 1.18/1.35 inference(skolemize,[status(sab)],[1255])).
% 1.18/1.35 tff(1257,plain,
% 1.18/1.35 (![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))),
% 1.18/1.35 inference(modus_ponens,[status(thm)],[1256, 1249])).
% 1.18/1.35 tff(1258,plain,
% 1.18/1.35 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | ((~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))) <=> ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(1259,plain,
% 1.18/1.35 ((tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 1.18/1.35 inference(rewrite,[status(thm)],[])).
% 1.18/1.35 tff(1260,plain,
% 1.18/1.35 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | ((~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[1259])).
% 1.18/1.36 tff(1261,plain,
% 1.18/1.36 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))))),
% 1.18/1.36 inference(transitivity,[status(thm)],[1260, 1258])).
% 1.18/1.36 tff(1262,plain,
% 1.18/1.36 ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | (tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(1263,plain,
% 1.18/1.36 ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))) | tptp_fun__E_(f(g(g(g(g(elem!0))))), f(g(g(g(g(g(elem!0)))))))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 1.18/1.36 tff(1264,plain,
% 1.18/1.36 ((~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1263, 1257, 651])).
% 1.18/1.36 tff(1265,plain,
% 1.18/1.36 ($false),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1264, 1247, 1231])).
% 1.18/1.36 tff(1266,plain,(tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.36 tff(1267,plain,
% 1.18/1.36 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1266, 1192])).
% 1.18/1.36 tff(1268,plain,
% 1.18/1.36 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1267, 1049])).
% 1.18/1.36 tff(1269,plain,
% 1.18/1.36 (^[A_17: $i] : refl((tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17)))) <=> (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17)))))),
% 1.18/1.36 inference(bind,[status(th)],[])).
% 1.18/1.36 tff(1270,plain,
% 1.18/1.36 (![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17)))) <=> ![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))),
% 1.18/1.36 inference(quant_intro,[status(thm)],[1269])).
% 1.18/1.36 tff(1271,plain,
% 1.18/1.36 (![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17)))) <=> ![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(1272,plain,
% 1.18/1.36 (^[A_17: $i] : rewrite((((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17))))) | tptp_fun__E_(f(A_17), f(g(A_17)))) <=> (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17)))))),
% 1.18/1.36 inference(bind,[status(th)],[])).
% 1.18/1.36 tff(1273,plain,
% 1.18/1.36 (![A_17: $i] : (((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17))))) | tptp_fun__E_(f(A_17), f(g(A_17)))) <=> ![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))),
% 1.18/1.36 inference(quant_intro,[status(thm)],[1272])).
% 1.18/1.36 tff(1274,axiom,(![A_17: $i] : (((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17))))) | tptp_fun__E_(f(A_17), f(g(A_17))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_40_23')).
% 1.18/1.36 tff(1275,plain,
% 1.18/1.36 (![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[1274, 1273])).
% 1.18/1.36 tff(1276,plain,
% 1.18/1.36 (![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[1275, 1271])).
% 1.18/1.36 tff(1277,plain,(
% 1.18/1.36 ![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))),
% 1.18/1.36 inference(skolemize,[status(sab)],[1276])).
% 1.18/1.36 tff(1278,plain,
% 1.18/1.36 (![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[1277, 1270])).
% 1.18/1.36 tff(1279,plain,
% 1.18/1.36 (((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(1280,plain,
% 1.18/1.36 ((tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.36 inference(rewrite,[status(thm)],[])).
% 1.18/1.36 tff(1281,plain,
% 1.18/1.36 (((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.18/1.36 inference(monotonicity,[status(thm)],[1280])).
% 1.18/1.36 tff(1282,plain,
% 1.18/1.36 (((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.36 inference(transitivity,[status(thm)],[1281, 1279])).
% 1.18/1.36 tff(1283,plain,
% 1.18/1.36 ((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.18/1.36 inference(quant_inst,[status(thm)],[])).
% 1.18/1.36 tff(1284,plain,
% 1.18/1.36 ((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.18/1.36 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 1.18/1.36 tff(1285,plain,
% 1.18/1.36 ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0))))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1284, 1278, 1092])).
% 1.18/1.36 tff(1286,plain,
% 1.18/1.36 (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1285, 1268])).
% 1.18/1.36 tff(1287,assumption,(~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))), introduced(assumption)).
% 1.18/1.36 tff(1288,plain,
% 1.18/1.36 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[636, 1287, 614])).
% 1.18/1.36 tff(1289,plain,
% 1.18/1.36 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[890, 1287, 614])).
% 1.18/1.36 tff(1290,plain,
% 1.18/1.36 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[882, 1289])).
% 1.18/1.36 tff(1291,plain,
% 1.18/1.36 (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[744, 1290])).
% 1.18/1.36 tff(1292,plain,
% 1.18/1.36 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[704, 1291, 1288])).
% 1.18/1.36 tff(1293,plain,
% 1.18/1.36 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1009, 1291, 1288])).
% 1.18/1.36 tff(1294,plain,
% 1.18/1.36 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1018, 1293])).
% 1.18/1.36 tff(1295,plain,
% 1.18/1.36 (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[1026, 1294])).
% 1.18/1.36 tff(1296,plain,
% 1.18/1.36 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[977, 1295, 1292])).
% 1.18/1.36 tff(1297,plain,
% 1.18/1.36 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[935, 1296])).
% 1.18/1.36 tff(1298,plain,
% 1.18/1.36 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[965, 1295, 1292])).
% 1.18/1.36 tff(1299,plain,
% 1.18/1.36 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[822, 1298])).
% 1.18/1.36 tff(1300,plain,
% 1.18/1.36 ($false),
% 1.18/1.36 inference(unit_resolution,[status(thm)],[989, 1299, 1297])).
% 1.18/1.36 tff(1301,plain,(tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.36 tff(1302,plain,
% 1.18/1.36 (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[1301, 614])).
% 1.20/1.36 tff(1303,plain,
% 1.20/1.36 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(1304,plain,
% 1.20/1.36 ((tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(1305,plain,
% 1.20/1.36 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.36 inference(monotonicity,[status(thm)],[1304])).
% 1.20/1.36 tff(1306,plain,
% 1.20/1.36 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.36 inference(transitivity,[status(thm)],[1305, 1303])).
% 1.20/1.36 tff(1307,plain,
% 1.20/1.36 ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(1308,plain,
% 1.20/1.36 ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[1307, 1306])).
% 1.20/1.36 tff(1309,plain,
% 1.20/1.36 ((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(elem!0))))))))),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[1308, 661, 1092])).
% 1.20/1.36 tff(1310,plain,
% 1.20/1.36 (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[1309, 1302])).
% 1.20/1.36 tff(1311,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|))))))))), introduced(assumption)).
% 1.20/1.36 tff(1312,assumption,(~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0))))))))), introduced(assumption)).
% 1.20/1.36 tff(1313,plain,
% 1.20/1.36 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(1314,plain,
% 1.20/1.36 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(1315,plain,
% 1.20/1.36 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.36 inference(monotonicity,[status(thm)],[1314])).
% 1.20/1.36 tff(1316,plain,
% 1.20/1.36 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.36 inference(transitivity,[status(thm)],[1315, 1313])).
% 1.20/1.36 tff(1317,plain,
% 1.20/1.36 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(1318,plain,
% 1.20/1.36 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[1317, 1316])).
% 1.20/1.36 tff(1319,plain,
% 1.20/1.36 ((~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|))))))))),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[1318, 629, 1052])).
% 1.20/1.36 tff(1320,plain,
% 1.20/1.36 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[1319, 1312, 1311])).
% 1.20/1.36 tff(1321,plain,
% 1.20/1.36 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[882, 1320])).
% 1.20/1.36 tff(1322,plain,
% 1.20/1.36 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(1323,plain,
% 1.20/1.36 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.36 inference(quant_inst,[status(thm)],[])).
% 1.20/1.36 tff(1324,plain,
% 1.20/1.36 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.36 inference(modus_ponens,[status(thm)],[1323, 1322])).
% 1.20/1.36 tff(1325,plain,
% 1.20/1.36 ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[1324, 629])).
% 1.20/1.36 tff(1326,plain,
% 1.20/1.36 (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[1325, 446])).
% 1.20/1.36 tff(1327,plain,
% 1.20/1.36 (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.36 inference(unit_resolution,[status(thm)],[1326, 1312, 1311])).
% 1.20/1.36 tff(1328,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|)))))))))), introduced(assumption)).
% 1.20/1.36 tff(1329,assumption,(~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0))))))))), introduced(assumption)).
% 1.20/1.36 tff(1330,plain,
% 1.20/1.36 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(1331,plain,
% 1.20/1.36 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.36 inference(rewrite,[status(thm)],[])).
% 1.20/1.36 tff(1332,plain,
% 1.20/1.36 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.36 inference(monotonicity,[status(thm)],[1331])).
% 1.20/1.36 tff(1333,plain,
% 1.20/1.36 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.37 inference(transitivity,[status(thm)],[1332, 1330])).
% 1.20/1.37 tff(1334,plain,
% 1.20/1.37 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(1335,plain,
% 1.20/1.37 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[1334, 1333])).
% 1.20/1.37 tff(1336,plain,
% 1.20/1.37 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1335, 686, 1052])).
% 1.20/1.37 tff(1337,plain,
% 1.20/1.37 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1336, 1329, 1328])).
% 1.20/1.37 tff(1338,assumption,(~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))), introduced(assumption)).
% 1.20/1.37 tff(1339,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), introduced(assumption)).
% 1.20/1.37 tff(1340,plain,
% 1.20/1.37 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[879, 1339, 1338])).
% 1.20/1.37 tff(1341,plain,
% 1.20/1.37 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(elem!0))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[836, 1340])).
% 1.20/1.37 tff(1342,plain,
% 1.20/1.37 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[783, 1339, 1338])).
% 1.20/1.37 tff(1343,plain,
% 1.20/1.37 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[861, 1342])).
% 1.20/1.37 tff(1344,plain,
% 1.20/1.37 ($false),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[869, 1343, 1341])).
% 1.20/1.37 tff(1345,plain,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.37 tff(1346,plain,
% 1.20/1.37 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1345, 1337])).
% 1.20/1.37 tff(1347,plain,
% 1.20/1.37 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(1348,plain,
% 1.20/1.37 (((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(1349,plain,
% 1.20/1.37 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[1348])).
% 1.20/1.37 tff(1350,plain,
% 1.20/1.37 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.37 inference(transitivity,[status(thm)],[1349, 1347])).
% 1.20/1.37 tff(1351,plain,
% 1.20/1.37 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(1352,plain,
% 1.20/1.37 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 1.20/1.37 tff(1353,plain,
% 1.20/1.37 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1352, 686, 446])).
% 1.20/1.37 tff(1354,plain,
% 1.20/1.37 (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1353, 1329, 1328])).
% 1.20/1.37 tff(1355,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), introduced(assumption)).
% 1.20/1.37 tff(1356,assumption,(~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0))))))))), introduced(assumption)).
% 1.20/1.37 tff(1357,plain,
% 1.20/1.37 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(1358,plain,
% 1.20/1.37 ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(1359,plain,
% 1.20/1.37 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[1358])).
% 1.20/1.37 tff(1360,plain,
% 1.20/1.37 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.20/1.37 inference(transitivity,[status(thm)],[1359, 1357])).
% 1.20/1.37 tff(1361,plain,
% 1.20/1.37 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(1362,plain,
% 1.20/1.37 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[1361, 1360])).
% 1.20/1.37 tff(1363,plain,
% 1.20/1.37 (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1362, 776, 446])).
% 1.20/1.37 tff(1364,plain,
% 1.20/1.37 (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1363, 1356, 1355])).
% 1.20/1.37 tff(1365,plain,
% 1.20/1.37 (((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(1366,plain,
% 1.20/1.37 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(1367,plain,
% 1.20/1.37 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[1366, 1365])).
% 1.20/1.37 tff(1368,plain,
% 1.20/1.37 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1367, 818])).
% 1.20/1.37 tff(1369,plain,
% 1.20/1.37 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1368, 1364])).
% 1.20/1.37 tff(1370,plain,
% 1.20/1.37 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(1371,plain,
% 1.20/1.37 ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(1372,plain,
% 1.20/1.37 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[1371])).
% 1.20/1.37 tff(1373,plain,
% 1.20/1.37 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.37 inference(transitivity,[status(thm)],[1372, 1370])).
% 1.20/1.37 tff(1374,plain,
% 1.20/1.37 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(1375,plain,
% 1.20/1.37 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 1.20/1.37 tff(1376,plain,
% 1.20/1.37 (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1375, 776, 1052])).
% 1.20/1.37 tff(1377,plain,
% 1.20/1.37 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1376, 1356, 1355])).
% 1.20/1.37 tff(1378,plain,
% 1.20/1.37 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[861, 1377])).
% 1.20/1.37 tff(1379,plain,
% 1.20/1.37 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(1380,plain,
% 1.20/1.37 ((tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0))))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.37 inference(rewrite,[status(thm)],[])).
% 1.20/1.37 tff(1381,plain,
% 1.20/1.37 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0)))))))))))),
% 1.20/1.37 inference(monotonicity,[status(thm)],[1380])).
% 1.20/1.37 tff(1382,plain,
% 1.20/1.37 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.37 inference(transitivity,[status(thm)],[1381, 1379])).
% 1.20/1.37 tff(1383,plain,
% 1.20/1.37 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.37 inference(quant_inst,[status(thm)],[])).
% 1.20/1.37 tff(1384,plain,
% 1.20/1.37 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.37 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 1.20/1.37 tff(1385,plain,
% 1.20/1.37 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1384, 847, 1092])).
% 1.20/1.37 tff(1386,plain,
% 1.20/1.37 ($false),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1385, 1378, 1369])).
% 1.20/1.37 tff(1387,plain,(tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.37 tff(1388,plain,
% 1.20/1.37 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.37 inference(unit_resolution,[status(thm)],[1387, 1354])).
% 1.20/1.37 tff(1389,plain,
% 1.20/1.37 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(1390,plain,
% 1.20/1.38 ((tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0))))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(1391,plain,
% 1.20/1.38 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[1390])).
% 1.20/1.38 tff(1392,plain,
% 1.20/1.38 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.38 inference(transitivity,[status(thm)],[1391, 1389])).
% 1.20/1.38 tff(1393,plain,
% 1.20/1.38 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(1394,plain,
% 1.20/1.38 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[1393, 1392])).
% 1.20/1.38 tff(1395,plain,
% 1.20/1.38 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1394, 794, 1092])).
% 1.20/1.38 tff(1396,plain,
% 1.20/1.38 ($false),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1395, 1388, 1346])).
% 1.20/1.38 tff(1397,plain,(tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(s(|'0'|)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.38 tff(1398,plain,
% 1.20/1.38 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1397, 1327])).
% 1.20/1.38 tff(1399,plain,
% 1.20/1.38 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(1400,plain,
% 1.20/1.38 ((tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0))))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(1401,plain,
% 1.20/1.38 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[1400])).
% 1.20/1.38 tff(1402,plain,
% 1.20/1.38 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.38 inference(transitivity,[status(thm)],[1401, 1399])).
% 1.20/1.38 tff(1403,plain,
% 1.20/1.38 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(1404,plain,
% 1.20/1.38 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[1403, 1402])).
% 1.20/1.38 tff(1405,plain,
% 1.20/1.38 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1404, 717, 1092])).
% 1.20/1.38 tff(1406,plain,
% 1.20/1.38 ($false),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1405, 1398, 1321])).
% 1.20/1.38 tff(1407,plain,(tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|))))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.38 tff(1408,plain,
% 1.20/1.38 (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|))))))))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1407, 1310])).
% 1.20/1.38 tff(1409,assumption,(~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))), introduced(assumption)).
% 1.20/1.38 tff(1410,assumption,(~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))), introduced(assumption)).
% 1.20/1.38 tff(1411,plain,
% 1.20/1.38 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(1412,plain,
% 1.20/1.38 ((tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))))) <=> (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(1413,plain,
% 1.20/1.38 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[1412])).
% 1.20/1.38 tff(1414,plain,
% 1.20/1.38 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.38 inference(transitivity,[status(thm)],[1413, 1411])).
% 1.20/1.38 tff(1415,plain,
% 1.20/1.38 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(1416,plain,
% 1.20/1.38 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[1415, 1414])).
% 1.20/1.38 tff(1417,plain,
% 1.20/1.38 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1416, 1205, 1052])).
% 1.20/1.38 tff(1418,plain,
% 1.20/1.38 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1417, 1410, 1409])).
% 1.20/1.38 tff(1419,plain,
% 1.20/1.38 (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1246, 1418, 1193])).
% 1.20/1.38 tff(1420,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|))))))))), introduced(assumption)).
% 1.20/1.38 tff(1421,plain,
% 1.20/1.38 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(1422,plain,
% 1.20/1.38 ((tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))))) <=> (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(1423,plain,
% 1.20/1.38 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.38 inference(monotonicity,[status(thm)],[1422])).
% 1.20/1.38 tff(1424,plain,
% 1.20/1.38 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.38 inference(transitivity,[status(thm)],[1423, 1421])).
% 1.20/1.38 tff(1425,plain,
% 1.20/1.38 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(1426,plain,
% 1.20/1.38 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[1425, 1424])).
% 1.20/1.38 tff(1427,plain,
% 1.20/1.38 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1426, 1205, 446])).
% 1.20/1.38 tff(1428,plain,
% 1.20/1.38 (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1427, 1410, 1409])).
% 1.20/1.38 tff(1429,plain,
% 1.20/1.38 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(1430,plain,
% 1.20/1.38 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.38 inference(quant_inst,[status(thm)],[])).
% 1.20/1.38 tff(1431,plain,
% 1.20/1.38 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.38 inference(modus_ponens,[status(thm)],[1430, 1429])).
% 1.20/1.38 tff(1432,plain,
% 1.20/1.38 (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1431, 1223, 446])).
% 1.20/1.38 tff(1433,plain,
% 1.20/1.38 (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.38 inference(unit_resolution,[status(thm)],[1432, 1428, 1420])).
% 1.20/1.38 tff(1434,plain,
% 1.20/1.38 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | ((~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(1435,plain,
% 1.20/1.38 ((tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.38 inference(rewrite,[status(thm)],[])).
% 1.20/1.38 tff(1436,plain,
% 1.20/1.38 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | ((~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[1435])).
% 1.20/1.39 tff(1437,plain,
% 1.20/1.39 (((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))))) <=> ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.39 inference(transitivity,[status(thm)],[1436, 1434])).
% 1.20/1.39 tff(1438,plain,
% 1.20/1.39 ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | (tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(1439,plain,
% 1.20/1.39 ((~![A_14: $i] : (tptp_fun__E_(f(A_14), f(g(A_14))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(A_14)))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(A_14))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(f(g(g(g(g(g(elem!0)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1438, 1437])).
% 1.20/1.39 tff(1440,plain,
% 1.20/1.39 ((~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1439, 1257, 1092])).
% 1.20/1.39 tff(1441,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1440, 1433, 1419])).
% 1.20/1.39 tff(1442,plain,(tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(1443,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1442, 1408, 1286, 613, 1049])).
% 1.20/1.39 tff(1444,plain,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(1445,assumption,(tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))), introduced(assumption)).
% 1.20/1.39 tff(1446,assumption,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))), introduced(assumption)).
% 1.20/1.39 tff(1447,plain,
% 1.20/1.39 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1191, 564, 1164])).
% 1.20/1.39 tff(1448,plain,
% 1.20/1.39 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|)))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1212, 1194, 1195])).
% 1.20/1.39 tff(1449,plain,
% 1.20/1.39 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1450,plain,
% 1.20/1.39 (((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))))) <=> ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1451,plain,
% 1.20/1.39 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[1450])).
% 1.20/1.39 tff(1452,plain,
% 1.20/1.39 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))))),
% 1.20/1.39 inference(transitivity,[status(thm)],[1451, 1449])).
% 1.20/1.39 tff(1453,plain,
% 1.20/1.39 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(1454,plain,
% 1.20/1.39 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(g(elem!0)))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1453, 1452])).
% 1.20/1.39 tff(1455,plain,
% 1.20/1.39 ((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1454, 1223, 697])).
% 1.20/1.39 tff(1456,plain,
% 1.20/1.39 (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(elem!0))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1455, 1448, 1445])).
% 1.20/1.39 tff(1457,plain,
% 1.20/1.39 (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1238, 1194, 1195])).
% 1.20/1.39 tff(1458,plain,
% 1.20/1.39 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1459,plain,
% 1.20/1.39 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1460,plain,
% 1.20/1.39 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[1459])).
% 1.20/1.39 tff(1461,plain,
% 1.20/1.39 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.39 inference(transitivity,[status(thm)],[1460, 1458])).
% 1.20/1.39 tff(1462,plain,
% 1.20/1.39 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(1463,plain,
% 1.20/1.39 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(elem!0))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1462, 1461])).
% 1.20/1.39 tff(1464,plain,
% 1.20/1.39 (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0))))))) | tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1463, 1223, 758])).
% 1.20/1.39 tff(1465,plain,
% 1.20/1.39 (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1464, 1457, 1446])).
% 1.20/1.39 tff(1466,plain,
% 1.20/1.39 ($false),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1264, 1465, 1456])).
% 1.20/1.39 tff(1467,plain,(tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.39 tff(1468,plain,
% 1.20/1.39 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1467, 1447, 1446, 1445])).
% 1.20/1.39 tff(1469,plain,
% 1.20/1.39 (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1285, 1468])).
% 1.20/1.39 tff(1470,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))), introduced(assumption)).
% 1.20/1.39 tff(1471,plain,
% 1.20/1.39 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1427, 1470, 1409])).
% 1.20/1.39 tff(1472,plain,
% 1.20/1.39 (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1285, 1471])).
% 1.20/1.39 tff(1473,plain,
% 1.20/1.39 (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1467, 1472, 1446, 1445])).
% 1.20/1.39 tff(1474,plain,
% 1.20/1.39 (((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1475,plain,
% 1.20/1.39 ((tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1476,plain,
% 1.20/1.39 (((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[1475])).
% 1.20/1.39 tff(1477,plain,
% 1.20/1.39 (((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.39 inference(transitivity,[status(thm)],[1476, 1474])).
% 1.20/1.39 tff(1478,plain,
% 1.20/1.39 ((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | (tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(1479,plain,
% 1.20/1.39 ((~![A_17: $i] : (tptp_fun__E_(f(A_17), f(g(A_17))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(A_17)))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(A_17))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))) | tptp_fun__E_(f(g(g(g(g(g(g(elem!0))))))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 1.20/1.39 tff(1480,plain,
% 1.20/1.39 ((~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1479, 1278, 468])).
% 1.20/1.39 tff(1481,plain,
% 1.20/1.39 (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1480, 1471])).
% 1.20/1.39 tff(1482,plain,
% 1.20/1.39 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1483,plain,
% 1.20/1.39 ((tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))))) <=> ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1484,plain,
% 1.20/1.39 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[1483])).
% 1.20/1.39 tff(1485,plain,
% 1.20/1.39 (((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))))) <=> ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.39 inference(transitivity,[status(thm)],[1484, 1482])).
% 1.20/1.39 tff(1486,plain,
% 1.20/1.39 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.39 inference(quant_inst,[status(thm)],[])).
% 1.20/1.39 tff(1487,plain,
% 1.20/1.39 ((~![B_8: $i, A_13: $i] : (tptp_fun__LE_(f(B_8), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(B_8)) | (~iLEQ(A_13, B_8)) | (~tptp_fun__LE_(f(A_13), s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(g(g(g(g(elem!0)))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.39 inference(modus_ponens,[status(thm)],[1486, 1485])).
% 1.20/1.39 tff(1488,plain,
% 1.20/1.39 ((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|)))))) | tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1487, 1205, 458])).
% 1.20/1.39 tff(1489,plain,
% 1.20/1.39 (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1488, 1481, 1470])).
% 1.20/1.39 tff(1490,plain,
% 1.20/1.39 (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(|'0'|)))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1191, 1473, 564])).
% 1.20/1.39 tff(1491,plain,
% 1.20/1.39 (tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1153, 1490, 534])).
% 1.20/1.39 tff(1492,plain,
% 1.20/1.39 (~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[560, 1491])).
% 1.20/1.39 tff(1493,assumption,(~tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))), introduced(assumption)).
% 1.20/1.39 tff(1494,plain,
% 1.20/1.39 (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|)))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[543, 535, 1493])).
% 1.20/1.39 tff(1495,plain,
% 1.20/1.39 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[1181, 1494, 1166])).
% 1.20/1.39 tff(1496,assumption,(tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))), introduced(assumption)).
% 1.20/1.39 tff(1497,plain,
% 1.20/1.39 (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|)))))),
% 1.20/1.39 inference(unit_resolution,[status(thm)],[314, 535, 1493])).
% 1.20/1.39 tff(1498,plain,
% 1.20/1.39 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1499,plain,
% 1.20/1.39 (((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|)))))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.39 inference(rewrite,[status(thm)],[])).
% 1.20/1.39 tff(1500,plain,
% 1.20/1.39 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0)))))))))))),
% 1.20/1.39 inference(monotonicity,[status(thm)],[1499])).
% 1.20/1.39 tff(1501,plain,
% 1.20/1.39 (((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))))) <=> ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))))),
% 1.20/1.40 inference(transitivity,[status(thm)],[1500, 1498])).
% 1.20/1.40 tff(1502,plain,
% 1.20/1.40 ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | ((~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1503,plain,
% 1.20/1.40 ((~![A_16: $i, B_10: $i] : ((~iLEQ(A_16, B_10)) | tptp_fun__LE_(f(B_10), s(s(s(s(|'0'|))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(B_10)) | (~tptp_fun__LE_(f(A_16), s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0))))))))) | (~iLEQ(g(g(g(g(g(g(g(elem!0))))))), g(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1502, 1501])).
% 1.20/1.40 tff(1504,plain,
% 1.20/1.40 (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1503, 575, 198])).
% 1.20/1.40 tff(1505,plain,
% 1.20/1.40 (tptp_fun__E_(s(s(s(s(|'0'|)))), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1504, 1497, 1496])).
% 1.20/1.40 tff(1506,plain,
% 1.20/1.40 ($false),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[609, 1505, 1495])).
% 1.20/1.40 tff(1507,plain,(tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(s(s(|'0'|))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(|'0'|))), f(g(g(g(g(g(g(g(elem!0)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.40 tff(1508,plain,
% 1.20/1.40 (tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1507, 1492, 1489, 1473])).
% 1.20/1.40 tff(1509,plain,
% 1.20/1.40 (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(|'0'|))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1163, 1490, 534])).
% 1.20/1.40 tff(1510,plain,
% 1.20/1.40 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1059, 1509, 504])).
% 1.20/1.40 tff(1511,plain,
% 1.20/1.40 (~tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0)))))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[530, 1510])).
% 1.20/1.40 tff(1512,plain,
% 1.20/1.40 (tptp_fun__E_(s(s(|'0'|)), f(g(g(g(g(g(g(g(elem!0))))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(g(g(elem!0)))))))), s(s(s(|'0'|)))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[266, 247])).
% 1.20/1.40 tff(1513,plain,
% 1.20/1.40 ($false),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1512, 1511, 1508])).
% 1.20/1.40 tff(1514,plain,((~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.40 tff(1515,plain,
% 1.20/1.40 (~tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|)))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1514, 564, 1446, 1445, 1409])).
% 1.20/1.40 tff(1516,plain,
% 1.20/1.40 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1517,plain,
% 1.20/1.40 (((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))))) <=> (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1518,plain,
% 1.20/1.40 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[1517])).
% 1.20/1.40 tff(1519,plain,
% 1.20/1.40 (((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.40 inference(transitivity,[status(thm)],[1518, 1516])).
% 1.20/1.40 tff(1520,plain,
% 1.20/1.40 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | ((~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1521,plain,
% 1.20/1.40 ((~![B_6: $i, A_10: $i] : ((~iLEQ(A_10, B_6)) | tptp_fun__LE_(f(B_6), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(B_6)) | (~tptp_fun__LE_(f(A_10), s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | (~iLEQ(g(g(g(g(g(elem!0))))), g(g(g(g(g(g(elem!0)))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 1.20/1.40 tff(1522,plain,
% 1.20/1.40 (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(s(|'0'|))))))) | tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1521, 1223, 1052])).
% 1.20/1.40 tff(1523,plain,
% 1.20/1.40 (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1522, 1515, 1446])).
% 1.20/1.40 tff(1524,plain,
% 1.20/1.40 (~tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1440, 1523])).
% 1.20/1.40 tff(1525,plain,
% 1.20/1.40 (tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(|'0'|)))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1464, 1524, 1446])).
% 1.20/1.40 tff(1526,plain,
% 1.20/1.40 ($false),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1417, 1525, 1469, 1409])).
% 1.20/1.40 tff(1527,plain,(tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(|'0'|))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.40 tff(1528,plain,
% 1.20/1.40 (tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|)))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1527, 563])).
% 1.20/1.40 tff(1529,plain,
% 1.20/1.40 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1528, 1444, 613])).
% 1.20/1.40 tff(1530,assumption,(~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))), introduced(assumption)).
% 1.20/1.40 tff(1531,assumption,(tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))), introduced(assumption)).
% 1.20/1.40 tff(1532,plain,
% 1.20/1.40 (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[734, 1531, 615])).
% 1.20/1.40 tff(1533,plain,
% 1.20/1.40 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1534,plain,
% 1.20/1.40 (((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1535,plain,
% 1.20/1.40 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[1534])).
% 1.20/1.40 tff(1536,plain,
% 1.20/1.40 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))))),
% 1.20/1.40 inference(transitivity,[status(thm)],[1535, 1533])).
% 1.20/1.40 tff(1537,plain,
% 1.20/1.40 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(g(elem!0))), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1538,plain,
% 1.20/1.40 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1537, 1536])).
% 1.20/1.40 tff(1539,plain,
% 1.20/1.40 (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~iLEQ(g(g(g(elem!0))), g(g(g(elem!0)))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1538, 629])).
% 1.20/1.40 tff(1540,plain,
% 1.20/1.40 (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1539, 676])).
% 1.20/1.40 tff(1541,plain,
% 1.20/1.40 (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0)))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1540, 1531, 1530])).
% 1.20/1.40 tff(1542,plain,
% 1.20/1.40 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))))) <=> ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1543,plain,
% 1.20/1.40 ((tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1544,plain,
% 1.20/1.40 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0)))))))) <=> ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))))))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[1543])).
% 1.20/1.40 tff(1545,plain,
% 1.20/1.40 (((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0)))))))) <=> ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))))),
% 1.20/1.40 inference(transitivity,[status(thm)],[1544, 1542])).
% 1.20/1.40 tff(1546,plain,
% 1.20/1.40 ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0)))))))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1547,plain,
% 1.20/1.40 ((~![A_11: $i] : (tptp_fun__E_(f(A_11), f(g(A_11))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(A_11)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(A_11))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(g(elem!0)))), f(g(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))))),
% 1.20/1.40 inference(modus_ponens,[status(thm)],[1546, 1545])).
% 1.20/1.40 tff(1548,plain,
% 1.20/1.40 ((~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0)))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1547, 661, 707])).
% 1.20/1.40 tff(1549,plain,
% 1.20/1.40 ($false),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1548, 1541, 1532])).
% 1.20/1.40 tff(1550,plain,((~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.40 tff(1551,plain,
% 1.20/1.40 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1550, 1530, 615])).
% 1.20/1.40 tff(1552,assumption,(~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))), introduced(assumption)).
% 1.20/1.40 tff(1553,assumption,(tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), introduced(assumption)).
% 1.20/1.40 tff(1554,plain,
% 1.20/1.40 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))),
% 1.20/1.40 inference(unit_resolution,[status(thm)],[1000, 1553, 672])).
% 1.20/1.40 tff(1555,plain,
% 1.20/1.40 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1556,plain,
% 1.20/1.40 (((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.40 inference(rewrite,[status(thm)],[])).
% 1.20/1.40 tff(1557,plain,
% 1.20/1.40 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.20/1.40 inference(monotonicity,[status(thm)],[1556])).
% 1.20/1.40 tff(1558,plain,
% 1.20/1.40 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.40 inference(transitivity,[status(thm)],[1557, 1555])).
% 1.20/1.40 tff(1559,plain,
% 1.20/1.40 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(g(elem!0)), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.40 inference(quant_inst,[status(thm)],[])).
% 1.20/1.40 tff(1560,plain,
% 1.20/1.40 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 1.20/1.41 tff(1561,plain,
% 1.20/1.41 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~iLEQ(g(g(elem!0)), g(g(elem!0)))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1560, 686])).
% 1.20/1.41 tff(1562,plain,
% 1.20/1.41 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1561, 923])).
% 1.20/1.41 tff(1563,plain,
% 1.20/1.41 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1562, 1553, 1552])).
% 1.20/1.41 tff(1564,plain,
% 1.20/1.41 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1565,plain,
% 1.20/1.41 ((tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1566,plain,
% 1.20/1.41 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0)))))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1565])).
% 1.20/1.41 tff(1567,plain,
% 1.20/1.41 (((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0))))))) <=> ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1566, 1564])).
% 1.20/1.41 tff(1568,plain,
% 1.20/1.41 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0))))))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1569,plain,
% 1.20/1.41 ((~![A_8: $i] : (tptp_fun__E_(f(A_8), f(g(A_8))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(A_8)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(A_8))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))) | tptp_fun__E_(f(g(g(elem!0))), f(g(g(g(elem!0)))))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1568, 1567])).
% 1.20/1.41 tff(1570,plain,
% 1.20/1.41 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0))))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1569, 717, 950])).
% 1.20/1.41 tff(1571,plain,
% 1.20/1.41 ($false),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1570, 1563, 1554])).
% 1.20/1.41 tff(1572,plain,((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.41 tff(1573,plain,
% 1.20/1.41 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1572, 1552, 672])).
% 1.20/1.41 tff(1574,assumption,(~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), introduced(assumption)).
% 1.20/1.41 tff(1575,assumption,(tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))), introduced(assumption)).
% 1.20/1.41 tff(1576,assumption,(~iLEQ(g(elem!0), g(elem!0))), introduced(assumption)).
% 1.20/1.41 tff(1577,plain,
% 1.20/1.41 ((~![A_29: $i] : iLEQ(A_29, A_29)) | iLEQ(g(elem!0), g(elem!0))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1578,plain,
% 1.20/1.41 ($false),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1577, 101, 1576])).
% 1.20/1.41 tff(1579,plain,(iLEQ(g(elem!0), g(elem!0))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.41 tff(1580,plain,
% 1.20/1.41 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(elem!0), g(elem!0))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(elem!0), g(elem!0))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1581,plain,
% 1.20/1.41 ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | (~iLEQ(g(elem!0), g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(elem!0), g(elem!0))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1582,plain,
% 1.20/1.41 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | (~iLEQ(g(elem!0), g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(elem!0), g(elem!0)))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1581])).
% 1.20/1.41 tff(1583,plain,
% 1.20/1.41 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | (~iLEQ(g(elem!0), g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(elem!0), g(elem!0))))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1582, 1580])).
% 1.20/1.41 tff(1584,plain,
% 1.20/1.41 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | (~iLEQ(g(elem!0), g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1585,plain,
% 1.20/1.41 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~iLEQ(g(elem!0), g(elem!0)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1584, 1583])).
% 1.20/1.41 tff(1586,plain,
% 1.20/1.41 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1585, 776, 1579])).
% 1.20/1.41 tff(1587,plain,
% 1.20/1.41 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1586, 1575, 1574])).
% 1.20/1.41 tff(1588,plain,
% 1.20/1.41 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[913, 1575, 896])).
% 1.20/1.41 tff(1589,plain,
% 1.20/1.41 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1590,plain,
% 1.20/1.41 ((tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))))) <=> ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1591,plain,
% 1.20/1.41 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0))))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1590])).
% 1.20/1.41 tff(1592,plain,
% 1.20/1.41 (((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))))) <=> ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1591, 1589])).
% 1.20/1.41 tff(1593,plain,
% 1.20/1.41 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1594,plain,
% 1.20/1.41 ((~![A_5: $i] : (tptp_fun__E_(f(A_5), f(g(A_5))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(A_5)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(A_5))))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0))))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1593, 1592])).
% 1.20/1.41 tff(1595,plain,
% 1.20/1.41 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))) | tptp_fun__E_(f(g(elem!0)), f(g(g(elem!0))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1594, 794])).
% 1.20/1.41 tff(1596,plain,
% 1.20/1.41 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0)))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1595, 938])).
% 1.20/1.41 tff(1597,plain,
% 1.20/1.41 ($false),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1596, 1588, 1587])).
% 1.20/1.41 tff(1598,plain,((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.41 tff(1599,plain,
% 1.20/1.41 (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1598, 896, 1574])).
% 1.20/1.41 tff(1600,plain,
% 1.20/1.41 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[918, 1599])).
% 1.20/1.41 tff(1601,plain,
% 1.20/1.41 (^[A_26: $i] : refl((~tptp_fun__E_(f(A_26), f(g(A_26)))) <=> (~tptp_fun__E_(f(A_26), f(g(A_26)))))),
% 1.20/1.41 inference(bind,[status(th)],[])).
% 1.20/1.41 tff(1602,plain,
% 1.20/1.41 (![A_26: $i] : (~tptp_fun__E_(f(A_26), f(g(A_26)))) <=> ![A_26: $i] : (~tptp_fun__E_(f(A_26), f(g(A_26))))),
% 1.20/1.41 inference(quant_intro,[status(thm)],[1601])).
% 1.20/1.41 tff(1603,plain,
% 1.20/1.41 (![A_26: $i] : (~tptp_fun__E_(f(A_26), f(g(A_26)))) <=> ![A_26: $i] : (~tptp_fun__E_(f(A_26), f(g(A_26))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1604,axiom,(![A_26: $i] : (~tptp_fun__E_(f(A_26), f(g(A_26))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause_19_05')).
% 1.20/1.41 tff(1605,plain,
% 1.20/1.41 (![A_26: $i] : (~tptp_fun__E_(f(A_26), f(g(A_26))))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 1.20/1.41 tff(1606,plain,(
% 1.20/1.41 ![A_26: $i] : (~tptp_fun__E_(f(A_26), f(g(A_26))))),
% 1.20/1.41 inference(skolemize,[status(sab)],[1605])).
% 1.20/1.41 tff(1607,plain,
% 1.20/1.41 (![A_26: $i] : (~tptp_fun__E_(f(A_26), f(g(A_26))))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1606, 1602])).
% 1.20/1.41 tff(1608,plain,
% 1.20/1.41 ((~![A_26: $i] : (~tptp_fun__E_(f(A_26), f(g(A_26))))) | (~tptp_fun__E_(f(elem!0), f(g(elem!0))))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1609,plain,
% 1.20/1.41 (~tptp_fun__E_(f(elem!0), f(g(elem!0)))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1608, 1607])).
% 1.20/1.41 tff(1610,plain,
% 1.20/1.41 (((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(elem!0))))) <=> ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(elem!0))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1611,plain,
% 1.20/1.41 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | (tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(elem!0))))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1612,plain,
% 1.20/1.41 ((~![A_2: $i] : (tptp_fun__E_(f(A_2), f(g(A_2))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(A_2)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A_2))))) | tptp_fun__E_(f(elem!0), f(g(elem!0))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(elem!0)))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1611, 1610])).
% 1.20/1.41 tff(1613,plain,
% 1.20/1.41 ((~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))) | (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(elem!0)))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1612, 847, 1609])).
% 1.20/1.41 tff(1614,plain,
% 1.20/1.41 (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(elem!0))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1613, 1600])).
% 1.20/1.41 tff(1615,plain,
% 1.20/1.41 (((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1616,plain,
% 1.20/1.41 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1617,plain,
% 1.20/1.41 ((~![A: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(A)) | tptp_fun__LE_(f(A), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1616, 1615])).
% 1.20/1.41 tff(1618,plain,
% 1.20/1.41 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(elem!0)) | tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1617, 818])).
% 1.20/1.41 tff(1619,plain,
% 1.20/1.41 (tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1618, 1614])).
% 1.20/1.41 tff(1620,plain,
% 1.20/1.41 ((~![A_23: $i] : iLEQ(A_23, g(A_23))) | iLEQ(elem!0, g(elem!0))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1621,plain,
% 1.20/1.41 (iLEQ(elem!0, g(elem!0))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1620, 81])).
% 1.20/1.41 tff(1622,plain,
% 1.20/1.41 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | ((~iLEQ(elem!0, g(elem!0))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~iLEQ(elem!0, g(elem!0))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1623,plain,
% 1.20/1.41 ((tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~iLEQ(elem!0, g(elem!0))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1624,plain,
% 1.20/1.41 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | ((~iLEQ(elem!0, g(elem!0))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))))),
% 1.20/1.41 inference(monotonicity,[status(thm)],[1623])).
% 1.20/1.41 tff(1625,plain,
% 1.20/1.41 (((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) <=> ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~iLEQ(elem!0, g(elem!0))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.20/1.41 inference(transitivity,[status(thm)],[1624, 1622])).
% 1.20/1.41 tff(1626,plain,
% 1.20/1.41 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | (~iLEQ(elem!0, g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))),
% 1.20/1.41 inference(quant_inst,[status(thm)],[])).
% 1.20/1.41 tff(1627,plain,
% 1.20/1.41 ((~![A_1: $i, B_0: $i] : (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(B_0)) | (~iLEQ(A_1, B_0)) | tptp_fun__LE_(f(B_0), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(A_1), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))))) | (~iLEQ(elem!0, g(elem!0))) | tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.41 inference(modus_ponens,[status(thm)],[1626, 1625])).
% 1.20/1.41 tff(1628,plain,
% 1.20/1.41 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | (~tptp_fun__LE_(f(elem!0), s(s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1627, 776, 1621])).
% 1.20/1.41 tff(1629,plain,
% 1.20/1.41 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(elem!0)))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1628, 1619, 1574])).
% 1.20/1.41 tff(1630,plain,
% 1.20/1.41 (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[945, 1600])).
% 1.20/1.41 tff(1631,plain,
% 1.20/1.41 (tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[935, 1630])).
% 1.20/1.41 tff(1632,plain,
% 1.20/1.41 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[930, 1631, 896])).
% 1.20/1.41 tff(1633,plain,
% 1.20/1.41 ($false),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1596, 1632, 1629])).
% 1.20/1.41 tff(1634,plain,(tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.41 tff(1635,plain,
% 1.20/1.41 (tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.41 inference(unit_resolution,[status(thm)],[1634, 1573])).
% 1.20/1.41 tff(1636,plain,
% 1.20/1.41 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1637,plain,
% 1.20/1.41 (((~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.41 inference(rewrite,[status(thm)],[])).
% 1.20/1.41 tff(1638,plain,
% 1.20/1.41 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[1637])).
% 1.20/1.42 tff(1639,plain,
% 1.20/1.42 (((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) <=> ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.42 inference(transitivity,[status(thm)],[1638, 1636])).
% 1.20/1.42 tff(1640,plain,
% 1.20/1.42 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | ((~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))),
% 1.20/1.42 inference(quant_inst,[status(thm)],[])).
% 1.20/1.42 tff(1641,plain,
% 1.20/1.42 ((~![A_4: $i, B_2: $i] : ((~iLEQ(A_4, B_2)) | tptp_fun__LE_(f(B_2), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(B_2)) | (~tptp_fun__LE_(f(A_4), s(s(s(s(s(s(s(s(s(|'0'|))))))))))))) | (~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | (~iLEQ(g(elem!0), g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.42 inference(modus_ponens,[status(thm)],[1640, 1639])).
% 1.20/1.42 tff(1642,plain,
% 1.20/1.42 ((~tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(|'0'|))))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0)))) | tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1641, 686, 906])).
% 1.20/1.42 tff(1643,plain,
% 1.20/1.42 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(elem!0))))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1642, 1635, 1552])).
% 1.20/1.42 tff(1644,plain,
% 1.20/1.42 (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1570, 1643])).
% 1.20/1.42 tff(1645,plain,
% 1.20/1.42 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[693, 1644, 672])).
% 1.20/1.42 tff(1646,plain,
% 1.20/1.42 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[980, 1645, 1573])).
% 1.20/1.42 tff(1647,plain,
% 1.20/1.42 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[935, 1646])).
% 1.20/1.42 tff(1648,plain,
% 1.20/1.42 (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(elem!0)))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[945, 1647])).
% 1.20/1.42 tff(1649,plain,
% 1.20/1.42 (tptp_fun__LE_(f(g(elem!0)), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[918, 1648])).
% 1.20/1.42 tff(1650,plain,
% 1.20/1.42 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(elem!0))))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[913, 1649, 1573])).
% 1.20/1.42 tff(1651,plain,
% 1.20/1.42 (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[989, 1647])).
% 1.20/1.42 tff(1652,plain,
% 1.20/1.42 (tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[822, 1651])).
% 1.20/1.42 tff(1653,plain,
% 1.20/1.42 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[965, 1652, 1645])).
% 1.20/1.42 tff(1654,plain,
% 1.20/1.42 ($false),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[957, 1653, 1650])).
% 1.20/1.42 tff(1655,plain,(tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(|'0'|)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.20/1.42 tff(1656,plain,
% 1.20/1.42 (tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.20/1.42 inference(unit_resolution,[status(thm)],[1655, 1551])).
% 1.20/1.42 tff(1657,plain,
% 1.20/1.42 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1658,plain,
% 1.20/1.42 (((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|))))))))))) <=> ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 1.20/1.42 inference(rewrite,[status(thm)],[])).
% 1.20/1.42 tff(1659,plain,
% 1.20/1.42 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0)))))))),
% 1.20/1.42 inference(monotonicity,[status(thm)],[1658])).
% 1.20/1.42 tff(1660,plain,
% 1.20/1.42 (((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))))) <=> ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0))))))),
% 1.26/1.42 inference(transitivity,[status(thm)],[1659, 1657])).
% 1.26/1.42 tff(1661,plain,
% 1.26/1.42 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | ((~iLEQ(g(g(elem!0)), g(g(g(elem!0))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.26/1.42 inference(quant_inst,[status(thm)],[])).
% 1.26/1.42 tff(1662,plain,
% 1.26/1.42 ((~![A_7: $i, B_4: $i] : ((~iLEQ(A_7, B_4)) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(B_4)) | tptp_fun__LE_(f(B_4), s(s(s(s(s(s(s(|'0'|)))))))) | (~tptp_fun__LE_(f(A_7), s(s(s(s(s(s(s(s(|'0'|)))))))))))) | (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | (~iLEQ(g(g(elem!0)), g(g(g(elem!0)))))),
% 1.26/1.42 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 1.26/1.42 tff(1663,plain,
% 1.26/1.42 ((~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(|'0'|)))))))))) | tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0))))) | tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|))))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1662, 629, 970])).
% 1.26/1.42 tff(1664,plain,
% 1.26/1.42 (tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(elem!0)))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1663, 1656, 1530])).
% 1.26/1.42 tff(1665,plain,
% 1.26/1.42 (~tptp_fun__E_(s(s(s(s(s(s(s(|'0'|))))))), f(g(g(g(g(elem!0))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1548, 1664])).
% 1.26/1.42 tff(1666,plain,
% 1.26/1.42 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(|'0'|)))))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[648, 1665, 615])).
% 1.26/1.42 tff(1667,plain,
% 1.26/1.42 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[726, 1666, 1551])).
% 1.26/1.42 tff(1668,plain,
% 1.26/1.42 (tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[992, 1667])).
% 1.26/1.42 tff(1669,plain,
% 1.26/1.42 (tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(elem!0)))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1000, 1668, 1551])).
% 1.26/1.42 tff(1670,plain,
% 1.26/1.42 (~tptp_fun__E_(s(s(s(s(s(s(s(s(|'0'|)))))))), f(g(g(g(g(elem!0))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[724, 1669])).
% 1.26/1.42 tff(1671,plain,
% 1.26/1.42 (~tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(s(s(|'0'|))))))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1009, 1670, 1666])).
% 1.26/1.42 tff(1672,plain,
% 1.26/1.42 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(g(elem!0))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1018, 1671])).
% 1.26/1.42 tff(1673,plain,
% 1.26/1.42 (~tptp_fun__E_(s(s(s(s(s(s(s(s(s(|'0'|))))))))), f(g(g(g(elem!0)))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1026, 1672])).
% 1.26/1.42 tff(1674,plain,
% 1.26/1.42 (~tptp_fun__LE_(f(g(g(elem!0))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[977, 1673, 1667])).
% 1.26/1.42 tff(1675,plain,
% 1.26/1.42 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(elem!0))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[935, 1674])).
% 1.26/1.42 tff(1676,plain,
% 1.26/1.42 (~tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[965, 1673, 1667])).
% 1.26/1.42 tff(1677,plain,
% 1.26/1.42 (tptp_fun__E_(s(s(s(s(s(s(s(s(s(s(|'0'|)))))))))), f(g(g(g(elem!0)))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[822, 1676])).
% 1.26/1.42 tff(1678,plain,
% 1.26/1.42 ($false),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[989, 1677, 1675])).
% 1.26/1.42 tff(1679,plain,(tptp_fun__LE_(f(g(g(g(elem!0)))), s(s(s(s(s(s(s(|'0'|)))))))) | tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))), inference(lemma,lemma(discharge,[]))).
% 1.26/1.42 tff(1680,plain,
% 1.26/1.42 (tptp_fun__LE_(f(g(g(g(g(elem!0))))), s(s(s(s(s(s(s(|'0'|))))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1679, 1529])).
% 1.26/1.42 tff(1681,plain,
% 1.26/1.42 (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(elem!0)))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1464, 1418, 1446])).
% 1.26/1.42 tff(1682,plain,
% 1.26/1.42 (tptp_fun__E_(s(s(s(s(s(s(|'0'|)))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1522, 1428, 1446])).
% 1.26/1.42 tff(1683,plain,
% 1.26/1.42 ($false),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1440, 1682, 1681])).
% 1.26/1.42 tff(1684,plain,(tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0)))))))) | (~tptp_fun__LE_(f(g(g(g(g(g(elem!0)))))), s(s(s(s(s(s(s(|'0'|))))))))) | tptp_fun__LE_(f(g(g(g(g(g(g(elem!0))))))), s(s(s(s(s(|'0'|))))))), inference(lemma,lemma(discharge,[]))).
% 1.26/1.42 tff(1685,plain,
% 1.26/1.42 (tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(g(elem!0))))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1684, 1444, 613])).
% 1.26/1.42 tff(1686,plain,
% 1.26/1.42 (~tptp_fun__E_(s(s(s(s(s(|'0'|))))), f(g(g(g(g(g(elem!0)))))))),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1285, 1685])).
% 1.26/1.42 tff(1687,plain,
% 1.26/1.42 ($false),
% 1.26/1.42 inference(unit_resolution,[status(thm)],[1267, 1686, 1680])).
% 1.26/1.42 % SZS output end Proof
% 1.26/1.42 % E exiting
%------------------------------------------------------------------------------